arXiv subjects

Leonid Petrov

Publications and source records attributed to Leonid Petrov.

At least 19 recordsLinked to original sources

arXiv2026

From Yang-Baxter to Robinson-Schensted-Knuth

We explain how to derive the Robinson-Schensted-Knuth (RSK) correspondence, a fundamental bijection in algebraic combinatorics, from the Yang-Baxter equation. The Yang-Baxter equation arose in the study of quantum many-body systems and later became a cornerstone of the theory of solvable lattice models, particularly vertex models. In a vertex model, arrows occupy the edges of a grid, and each vertex carries a Boltzmann weight determined by the arrows on the four edges meeting at it. The weight of a configuration is the product of these local weights, and a partition function is the sum of the weights of all configurations with prescribed boundary conditions. For a vertex model whose partition functions are the Schur polynomials, the two sides of each instance of the Yang-Baxter equation admit exactly one weight-preserving matching of their summands. Carried across a grid, this forced matching is the classical RSK correspondence in the form of Fomin's growth diagrams. In natural coordinates the local matching becomes the combinatorial three-dimensional R, a set-theoretic solution of the Zamolodchikov tetrahedron equation. Its periodic closure returns the combinatorial R-matrices of one-row crystals. The forced matching is special to the Schur weights. For the Hall-Littlewood and q-Whittaker deformations and their spin versions, at generic parameter values no deterministic matching works for all boundary data. Reading each instance of the Yang-Baxter equation probabilistically, we replace the matching by a coupling of the two sides - a bijectivization, or probabilistic bijection - and obtain Markov operators that transport probability measures attached to vertex models. Iterated over the grid, these operators produce randomized RSK-type dynamics and interacting particle systems, including q-PushTASEP and the stochastic six-vertex model.

math.CO↗

arXiv2026

Colored Interlacing Triangles and Genocchi Medians

Colored interlacing triangles, introduced by Aggarwal-Borodin-Wheeler (2024), provide the combinatorial framework for the central limit theorem for probability measures arising from the Lascoux-Leclerc-Thibon (LLT) polynomials. Colored interlacing triangles depend on two key parameters: the number of colors $n$ and the depth of the triangle $N$. Recent work of Gaetz-Gao (2025) connects these objects to Schubert calculus and resolves the enumeration for $n=3$ and arbitrary depth $N$. However, the enumerative behavior for general $n$ has remained open. In this paper, we analyze the complementary regime: fixed depth $N=2$ and arbitrary number of colors $n$. We prove that in this setting, colored interlacing triangles considered up to a simultaneous relabeling of the colors are in bijection with Dumont derangements, identifying their enumeration with the Genocchi medians. This connects the probabilistic model to a rich hierarchy of classical combinatorial objects. In particular, under this bijection, the natural decomposition of a triangle into consecutive indecomposable blocks corresponds to the direct-sum decomposition of the associated permutation (readily yielding a generating function identity). Using a recent bijection of Poddar, Sawant, and Shankar (2026), we further identify these 'indecomposable' triangles with pure D-permutations. Furthermore, we introduce a $q$-deformation of this enumeration arising naturally from the LLT transition energy. For identity bottom row, we show that the corresponding statistic is the sum of the lower-crossing and lower-nesting statistics on Dumont derangements, and is additive over indecomposable triangles. This yields a new $q$-analogue of the median Genocchi numbers with an elegant continued-fraction expansion, as well as an interpretation of the indecomposable enumerators as Boolean cumulants of a family of probability measures on $\mathbb R$.

math.CO↗

arXiv2026

Perturbed Beta Corners Process

We introduce and study the perturbed $β$-corners process, a deformation of the classical $β$-corners process. The latter is a probability measure on interlacing arrays of real numbers that, for the classical values $β=1,2,4$, describes the joint distribution of eigenvalues of principal submatrices of a Gaussian random matrix with the corresponding GOE/GUE/GSE symmetry. For classical $β$, the perturbed process arises from adding a deterministic diagonal matrix $A=diag(a_1,...,a_N)$ to a GOE/GUE/GSE matrix. The eigenvalues of the resulting random matrix depend symmetrically on $a_1,...,a_N$, but this symmetry does not extend to the whole corners process. We extend the construction to all $β>0$ via multivariate Bessel functions, and analyze the crystallization ($β\to\infty$) of the resulting interlacing array, proving a law of large numbers and a central limit theorem in two regimes. For fixed perturbation, the eigenvalue repulsion dominates, and the array crystallizes on the same lattice of polynomial-derivative roots, with the same discrete Gaussian free field fluctuations, as in the unperturbed case treated by Gorin and Marcus (arXiv:1706.07393). New phenomena appear in the second regime, where the $a_i$'s grow linearly in $β$. Then the external source competes with the repulsion at leading order. Here the array freezes on a deformed lattice characterized by a coupled system of optimality equations. The fluctuations are governed by the same discrete Gaussian free field, now attached to the deformed lattice. The deformed lattice equations decouple in the special case of a single spike in the last coordinate. Then the deformed lattice is obtained explicitly by applying one shifted derivative $D_c f = f' + cf$ followed by iterated ordinary derivatives.

math.PR↗

arXiv2026

A Borodin-Okounkov-Geronimo-Case identity for tilted Toeplitz minors

We prove a Fredholm determinantal identity for the tilted Toeplitz minor $$ D_{N}^{ξ,θ}(φ):= \det\bigl[(θ_{i}ξ_{j}φ)_{i-j}\bigr]_{i,j=1}^{N}, $$ generalizing the Borodin-Okounkov-Geronimo-Case (BOGC) identity to oblique splittings of the Hardy space. The tilts $ξ_{j},θ_{i}$ enter only through an oblique projection that multiplies the trace-class kernel $K$ inside the Fredholm determinant; the BOGC operator $A=I-K$ constructed from $φ$ is unchanged. Baik-Liao-Liu (arXiv:2603.01964) and Liu-Tripathi (arXiv:2604.24747) have recently shown that the same tilted Toeplitz minor admits a contour Fredholm-determinantal representation, in connection with the periodic Totally Asymmetric Simple Exclusion Process (TASEP). In the periodic TASEP application of Baik-Liao-Liu, the formula plays an important role in identifying the periodic KPZ fixed point with general initial data. Our formula is a companion to their Fredholm determinant and readily reduces to the original BOGC identity. The one-sided tilted Toeplitz minor (that is, when all $θ_i=1$) admits a bialternant form recovering Schur and Grothendieck polynomials as special cases. A Cauchy-Binet expansion realizes $D_{N}^{ξ,θ}$ as a restricted sum over partitions of products of Jacobi-Trudi type determinants, generalizing Gessel's theorem. In the pure-shift setting this specializes to a skew Schur expansion. Finally, for finite Laurent exponential symbols, we record explicit resolvent-block flow identities and formulate the associated finite-dimensional closure problem. We also illustrate a possible asymptotic application leading to finite-rank perturbations of the Airy kernel.

math.FA↗

arXiv2026

Computation and sampling for Schubert specializations

We present computational results on principal specializations $\mathfrak{S}_w(1^n)$ of Schubert polynomials, which count reduced pipe dreams and reduced bumpless pipe dreams (RBPD). We find the first counterexample, at $n=17$, to the Merzon-Smirnov conjecture (arXiv:1410.6857) that the maximum of $\mathfrak{S}_w(1^n)$ over $S_n$ is attained at a layered permutation. The simulations suggest that $\lim_{n \to \infty} \log(\max_{w\in S_n}\mathfrak{S}_w(1^n))/n^2$ equals the maximal layered permutations' constant from Morales-Pak-Panova (arXiv:1805.04341). We also explore the random permutation drawn from the distribution proportional to $\mathfrak{S}_w(1^n)$, revealing permuton-like asymptotics similar to those for Grothendieck polynomials by Morales-Panova-Petrov-Yeliussizov (arXiv:2407.21653). We implement and compare three recurrences for $\mathfrak{S}_w(1^n)$: the descent formula (Macdonald), transition formula (Lascoux--Schutzenberger), and cotransition formula (Knutson). For sampling uniformly random RBPDs (whose count is $\sum_{w\in S_n} \mathfrak{S}_w(1^n)$), we show that reducedness breaks the sublattice property of the ASM lattice, preventing monotone CFTP and causing false coalescence. We develop an efficient MCMC sampler with macroscopic "droop" updates for connectivity and fast mixing. Our code computes $\mathfrak{S}_w(1^n)$ up to $n\sim 20$ and samples random RBPDs up to $n\sim 60$ on a personal computer ($n\sim 100$ on a cluster).

math.CO↗

arXiv2026

Assessment of the Earth orientation parameter accuracy from concurrent VLBI observations

We have assessed accuracy of estimates of Earth orientation parameters (EOP) determined from several very long baseline interferometry (VLBI) observing programs that ran concurrently at different networks. We consider that the root mean square of differences in EOP estimates derived from concurrent observations is a reliable measure of accuracy. We confirmed that formal errors based on the assumption that the noise in observables is uncorrelated have a limited use. We found no evidence that advanced scheduling strategies with special considerations regarding the ability to better solve for atmospheric path in zenith direction applied for 1-hr single-baseline sessions have any measurable impact on the accuracy of EOP estimates. From this, we conclude that there is a certain limit in our ability to solve for the atmospheric path delay using microwave observations themselves and a scheduling strategy is not the factor that impairs accuracy of EOP determination. We determined that EOP errors vary with season, being smaller in winter and greater in summer. We got the quantitative estimate of the impact of unmodeled source structure on EOP estimates and we found that the seasonal extra variance is one order of magnitude greater than the impact of source structure. We have established that the EOP errors are scaled with an increase in duration of an observing session as a broken power law with the power of -0.3 at durations longer than 2-4 hours, which we explain as a manifestation of the presence of correlations in the atmospheric noise.

physics.geo-ph↗

arXiv2025

A unified model of feed rotation in radio telescopes and GNSS antennas

We describe a model that accounts for the phase rotation that occurs when a receiver or transmitter changes orientation while observing or emitting circularly polarized electromagnetic waves. This model extends work detailing Global Navigation Satellite Systems (GNSS) carrier phase wind-up to allow us to describe the interaction of changing satellite orientation with phase rotation in observing radio telescopes. This development is motivated by, and a critical requirement of, unifying GNSS and Very Long Baseline Interferometry (VLBI) measurements at the observation level. The model can be used for either stationary choke ring antennas or steerable radio telescopes observing either natural radio sources or satellites. Simulations and experimental data are used to validate the model and to illustrate its importance. In addition, we rigorously lay out the feed rotation correction for radio telescopes with beam waveguide and full Nasmyth focuses and validate the correction by observing the effect with dual polarization observations. Using this feed rotation model for beam waveguide telescopes, we produce the first phase delay solution for the VLBI baseline WARK30M-WARK12M. We provide a practical guide to using the feed rotation model in Appendix D.

astro-ph.IM↗

arXiv2025

Random Fibonacci Words via Clone Schur Functions

We study positivity and probabilistic properties arising from the Young--Fibonacci lattice $\mathbb{YF}$, a 1-differential poset on binary (Fibonacci) words of 1's and 2's, graded by digit sum. Building on Okada's theory of clone Schur functions (Trans. Amer. Math. Soc. 346 (1994), 549--568), we define clone coherent measures on $\mathbb{YF}$ that generate random Fibonacci words of increasing length; unlike for the Young lattice (powered by the classical Schur functions), clone coherent measures are generally not extremal on $\mathbb{YF}$. Our first main result is a complete characterization of Fibonacci positive specializations -- parameter sequences which yield positive clone Schur functions on $\mathbb{YF}$. Second, we connect Fibonacci positivity with: (i) total positivity of tridiagonal matrices; (ii) Stieltjes moment sequences; (iii) the combinatorics of set partitions; and (iv) families of univariate orthogonal polynomials from the (q-)Askey scheme. We further link moment sequences of orthogonal polynomials to combinatorial structures on Fibonacci words, a connection that may be of independent interest. Third, we analyze scaling limits of the induced random words, obtaining stick-breaking-type limits (linked to GEM laws), new dependent stick-breaking limits, and limits supported on the discrete part of the Martin boundary of $\mathbb{YF}$. These results significantly extend the asymptotics of the Plancherel measure on $\mathbb{YF}$ proved by Gnedin--Kerov (Math. Proc. Camb. Philos. Soc. 129 (2000), 433--446). Finally, we prove Cauchy-type identities for clone Schur functions with quadridiagonal-determinant right-hand side (in contrast to the product form for classical Schur functions), and construct models of random permutations and involutions from Fibonacci-positive specializations together with a Robinson--Schensted correspondence adapted to $\mathbb{YF}$.

math.PR↗

arXiv2025

Random Lozenge Waterfall: Dimensional Collapse of Gibbs Measures

We investigate the asymptotic behavior of the q-Racah probability measure on lozenge tilings of a hexagon whose side lengths scale linearly with a large parameter $L$, while the parameters $q\in(0,1)$ and $κ\in \mathbf{i}\mathbb{R}$ remain fixed. This regime differs fundamentally from the traditional case $q\sim e^{-c/L}\to1$, in which random tilings are locally governed by two-dimensional translation-invariant ergodic Gibbs measures. In the fixed-q regime we uncover a new macroscopic phase, the waterfall (previously only observed experimentally), where the two-dimensional Gibbs structure collapses into a one-dimensional random stepped interface that we call a barcode. We prove a law of large numbers and exponential concentration, showing that the random tilings converge to a deterministic waterfall profile. We further conjecture an explicit correlation kernel of the one-dimensional barcode process arising in the limit. Remarkably, the limit is invariant under shifts by $2\mathbb{Z}$ but not by $\mathbb{Z}$, exhibiting an emergent period-two structure absent from the original weights. Our conjectures are supported by extensive numerical evidence and perfect sampling simulations. The kernel is built from a family of functions orthogonal in both spaces $\ell^{2}(\mathbb{Z})$ and $\ell^{2}(\mathbb{Z}+\frac12)$, that may be of independent interest. Our proofs adapt the spectral projection method of Borodin-Gorin-Rains (arXiv:0905.0679) to the regime with fixed~q. The resulting asymptotic analysis is substantially more involved, and leads to non-self-adjoint operators. We overcome these challenges in the exponential concentration result by a separate argument based on sharp bounds for the ratios of probabilities under the q-Racah orthogonal polynomial ensemble.

math.PR↗

arXiv2025

Domino Tilings of the Aztec Diamond in Random Environment and Schur Generating Functions

We study the asymptotic behavior of random domino tilings of the Aztec diamond of size $M$ in a random environment, where the environment is a one-periodic sequence of i.i.d. random weights attached to domino positions (i.e., to the edges of the underlying portion of the square grid). We consider two cases: either the variance of the weights decreases at a critical scale $1/M$, or the distribution of the weights is fixed. In the former case, the unrescaled fluctuations of the domino height function are governed by the sum of a Gaussian Free Field and an independent Brownian motion. In the latter case, we establish fluctuations on the much larger scale $\sqrt M$, given by the Brownian motion alone. To access asymptotic fluctuations in random environment, we employ the method of Schur generating functions. Moreover, we substantially extend the known Law of Large Numbers and Central Limit Theorems for particle systems via Schur generating functions in order to apply them to our setting. These results might be of independent interest.

math.PR↗

arXiv2025

Colored Interacting Particle Systems on the Ring: Stationary Measures from Yang-Baxter Equation

Recently, there has been much progress in understanding stationary measures for colored (also called multi-species or multi-type) interacting particle systems, motivated by asymptotic phenomena and rich underlying algebraic and combinatorial structures (such as nonsymmetric Macdonald polynomials). In this paper, we present a unified approach to constructing stationary measures for most of the known colored particle systems on the ring and the line, including (1) the Asymmetric Simple Exclusion Process (multispecies ASEP, or mASEP); (2) the q-deformed Totally Asymmetric Zero Range Process (TAZRP) also known as the q-Boson particle system; (3) the q-deformed Pushing Totally Asymmetric Simple Exclusion Process (q-PushTASEP). Our method is based on integrable stochastic vertex models and the Yang-Baxter equation. We express the stationary measures as partition functions of new "queue vertex models" on the cylinder. The stationarity property is a direct consequence of the Yang-Baxter equation. For the mASEP on the ring, a particular case of our vertex model is equivalent to the multiline queues of Martin (arXiv:1810.10650). For the colored q-Boson process and the q-PushTASEP on the ring, we recover and generalize known stationary measures constructed using multiline queues or other methods by Ayyer-Mandelshtam-Martin (arXiv:2011.06117, arXiv:2209.09859), and Bukh-Cox (arXiv:1912.03510). Our proofs of stationarity use the Yang-Baxter equation and bypass the Matrix Product Ansatz used for the mASEP by Prolhac-Evans-Mallick (arXiv:0812.3293). On the line and in a quadrant, we use the Yang-Baxter equation to establish a general colored Burke's theorem, which implies that suitable specializations of our queue vertex models produce stationary measures for particle systems on the line. We also compute the colored particle currents in stationarity.

math.PR↗

arXiv2025

Grothendieck Shenanigans: Permutons from pipe dreams via integrable probability

We study random permutations arising from reduced pipe dreams. Our main model is motivated by Grothendieck polynomials with parameter $β=1$ arising in K-theory of the flag variety. The probability weight of a permutation is proportional to the principal specialization (setting all variables to 1) of the corresponding Grothendieck polynomial. By mapping this random permutation to a version of TASEP (Totally Asymmetric Simple Exclusion Process), we describe the limiting permuton and fluctuations around it as the order $n$ of the permutation grows to infinity. The fluctuations are of order $n^{\frac13}$ and have the Tracy-Widom GUE distribution, which places this algebraic (K-theoretic) model into the Kardar-Parisi-Zhang universality class. We also investigate non-reduced pipe dreams and make progress on a recent open problem on the asymptotic number of inversions of the resulting permutation. Inspired by Stanley's question for the maximal value of principal specializations of Schubert polynomials, we resolve the analogous question for $β=1$ Grothendieck polynomials, and provide bounds for general $β$.

math.PR↗

arXiv2025

The Radio Fundamental Catalogue. I. Astrometry

We present an all-sky catalog of absolute positions and estimates of correlated flux density of 21,942 compact radio sources determined from processing interferometric visibility data of virtually all very long baseline interferometry (VLBI) observing sessions at 2-23 GHz from 72 programs suitable for absolute astrometry collected for 30 years. We used a novel technique of generation of a data set of fused observables that allowed us to incorporate all available data in our analysis. The catalog is the most complete and most precise to date. It forms the foundation and reference for positional astronomy, space geodesy, space navigation, and population analysis of active galactic nuclei (AGNs), and provides calibrators for phase referencing for differential astrometry and VLBI astrophysical observations. Its accuracy was evaluated through a detailed accounting of systematic errors, rigorous decimation tests, comparison of different data sets, and comparison with other catalogs. The catalog preferentially samples AGNs with strong contemporary parsec-scale synchrotron emission. Its milliarcsecond-level positional accuracy allows association of these AGNs with detections in a wide range of the electromagnetic spectrum from low-frequency radio to gamma-rays and high-energy neutrinos. We describe the innovative data processing and calibration technique in full detail, report the in depth analysis of random and systematic positional errors, and provide a list of associations with large surveys at different wavelengths.

astro-ph.IM↗

arXiv2024

Extracting Geodetic Data from GNSS-VLBI Co-Observation

We have been developing a novel interferometer formed directly between a Very Long Baseline Interferometry (VLBI) radio telescope and a Global Navigation Satellite Systems (GNSS) antenna/receiver. This interferometer is enabled by the High Rate Tracking Receiver (HRTR), a high-performance GNSS software-defined receiver that records baseband data similar to a VLBI receiving system. Of particular interest is the potential of the technique to produce precise local tie vectors directly between the geodetic reference points of VLBI and GNSS antennas for use in the determination of combination terrestrial reference frames. In this paper, we will describe the unique setup of this interferometer before discussing current developmental work in estimating local tie vectors from experimental data collected using this technique. In particular, much recent work has been in exploring the possibility of direct comparison of the GNSS and VLBI processing techniques. A significant advantage of GNSS-VLBI co-observation of GNSS satellites comes from the ability to cross-check position and clock estimates derived from differential measurements in VLBI-style processing with differential GNSS processing and absolute GNSS positioning with Precise Point Positioning (PPP). We show a preliminary VLBI analysis of interferometric data including a differential positioning solution using phase delays.

physics.geo-ph↗

arXiv2024

Hook-length Formulas for Skew Shapes via Contour Integrals and Vertex Models

The number of standard Young tableaux of a skew shape $λ/μ$ can be computed as a sum over excited diagrams inside $λ$. Excited diagrams are in bijection with certain lozenge tilings, with flagged semistandard tableaux and also nonintersecting lattice paths inside $λ$. We give two new proofs of a multivariate generalization of this formula, which allow us to extend the setup beyond standard Young tableaux and the underlying Schur symmetric polynomials. The first proof uses multiple contour integrals. The second one interprets excited diagrams as configurations of a six-vertex model at a free fermion point, and derives the formula for the number of standard Young tableaux of a skew shape from the Yang-Baxter equation.

math.CO↗

arXiv2024

A millisecond pulsar position determined to 0.2 milliarcsecond precision with VLBI

Precise millisecond pulsar (MSP) positions determined with very long baseline interferometry (VLBI) hold the key to building the connection between the kinematic and dynamic reference frames respectively used by VLBI and pulsar timing. The frame connection would provide an important pathway to examining the planetary ephemerides used in pulsar timing, and potentially enhancing the sensitivities of pulsar timing arrays used to detect stochastic gravitational-wave background at nano-Hz regime. We aim at significantly improving the VLBI-based MSP position from its current $\gtrsim1\,$mas precision level by reducing the two dominant components in the positional uncertainty -- the propagation-related uncertainty and the uncertainty resulting from the frequency-dependent core shifts of the reference sources. We introduce a new differential astrometry strategy of using multiple calibrators observed at several widely separated frequencies, which we call PINPT (Phase-screen Interpolation plus frequeNcy-dePendent core shifT correction; read as "pinpoint") for brevity. The strategy allows determination of the core-shift and mitigates the impact of residual delay in the atmosphere. We implemented the strategy on PSR J2222-0137, an MSP well constrained astrometrically with VLBI and pulsar timing. Using the PINPT strategy, we determined core shifts for 4 AGNs around PSR J2222-0137, and derived a VLBI-based pulsar position with uncertainty of 0.17 mas and 0.32 mas in right ascension and declination, respectively, approaching the uncertainty level of the best-determined timing-based MSP positions. The realization of the PINPT strategy promises a factor-of-5 positional precision enhancement (over conventional VLBI astrometry) for all kinds of compact radio sources observed at $\lesssim2$ GHz, including most fast radio bursts.

astro-ph.IM↗

arXiv2024

The Black Hole Explorer: Operating a Hybrid Observatory

We present a baseline science operations plan for the Black Hole Explorer (BHEX), a space mission concept aiming to confirm the existence of the predicted sharp ``photon ring" resulting from strongly lensed photon trajectories around black holes, as predicted by general relativity, and to measure its size and shape to determine the black hole's spin. BHEX will co-observe with a ground-based very long baseline interferometric (VLBI) array at high-frequency radio wavelengths, providing unprecedented high resolution with the extension to space that will enable photon ring detection and studies of active galactic nuclei. Science operations require a simultaneous coordination between BHEX and a ground array of large and small radio apertures to provide opportunities for surveys and imaging of radio sources, while coordination with a growing network of optical downlink terminals provides the data rates necessary to build sensitivity on long baselines to space. Here we outline the concept of operations for the hybrid observatory, the available observing modes, the observation planning process, and data delivery to achieve the mission goals and meet mission requirements.

astro-ph.IM↗

arXiv2024

Radioastrometry at different frequencies

Very long baseline interferometry (VLBI) technique allows us to determine positions of thousands of radio sources using the absolute astrometry approach. I have investigated the impact of a selection of observing frequencies in a range from 2 to 43 GHz in single-band, dual-band, and quad-band observing modes on astrometric results. I processed seven datasets in a range of 72 thousands to 6.9 million observations, estimated source positions, and compared them. I found that source positions derived from dual-band, quad-band, and 23.6 GHz single-band data agree at a level below 0.2 mas. Comparison of independent datasets allowed me to assess the error level of individual catalogues: 0.05-0.07 mas per position component. Further comparison showed that individual catalogues have systematic errors at the same level. Positions from 23.6 GHz single-band data show systematic errors related to the residual ionosphere contribution. Analysis of source positions differences revealed systematic errors along the jet direction at a level of 0.09 mas. Network related systematic errors affect all the data regardless of frequency. Comparison of position estimates allowed me to derive the stochastic error model that closes the error budget. Based on collected evidence, I made a conclusion that development of frequency-dependent reference frames of the entire sky is not warranted. In most cases dual-band, quad-band, and single-band data at frequency 22 GHz and higher can be used interchangeably, which allows us to exploit the strength of a specific frequency setup for given objects. Mixing observations at different frequencies causes errors not exceeding 0.07 mas.

astro-ph.IM↗