arXiv subjects

Leonid Petrov

Publications and source records attributed to Leonid Petrov.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2024

Tilted biorthogonal ensembles, Grothendieck random partitions, and determinantal tests

We study probability measures on partitions based on symmetric Grothendieck polynomials. These deformations of Schur polynomials introduced in the K-theory of Grassmannians share many common properties. Our Grothendieck measures are analogs of the Schur measures on partitions introduced by Okounkov (arXiv:math/9907127 [math.RT]). Despite the similarity of determinantal formulas for the probability weights of Schur and Grothendieck measures, we demonstrate that Grothendieck measures are \emph{not} determinantal point processes. This question is related to the principal minor assignment problem in algebraic geometry, and we employ a determinantal test first obtained by Nanson in 1897 for the $4\times4$ problem. We also propose a procedure for getting Nanson-like determinantal tests for matrices of any size $n\ge4$ which appear new for $n\ge 5$. By placing the Grothendieck measures into a new framework of tilted biorthogonal ensembles generalizing a rich class of determinantal processes introduced by Borodin (arXiv:math/9804027 [math.CA]), we identify Grothendieck random partitions as a cross-section of a Schur process, a determinantal process in two dimensions. This identification expresses the correlation functions of Grothendieck measures through sums of Fredholm determinants, which are not immediately suitable for asymptotic analysis. A more direct approach allows us to obtain a limit shape result for the Grothendieck random partitions. The limit shape curve is not particularly explicit as it arises as a cross-section of the limit shape surface for the Schur process. The gradient of this surface is expressed through the argument of a complex root of a cubic equation.

math.PR↗

arXiv2023

First observations with a GNSS antenna to radio telescope interferometer

We describe the design of a radio interferometer composed of a Global Navigation Satellite Systems (GNSS) antenna and a Very Long Baseline Interferometry (VLBI) radio telescope. Our eventual goal is to use this interferometer for geodetic applications including local tie measurements. The GNSS element of the interferometer uses a unique software-defined receiving system and modified commercial geodetic-quality GNSS antenna. We ran three observing sessions in 2022 between a 25 m radio telescope in Fort Davis, Texas (FD-VLBA), a transportable GNSS antenna placed within 100 meters, and a GNSS antenna placed at a distance of about 9 km. We have detected a strong interferometric response with a Signal-to-Noise Ratio (SNR) of over 1000 from Global Positioning System (GPS) and Galileo satellites. We also observed natural radio sources including Galactic supernova remnants and Active Galactic Nuclei (AGN) located as far as one gigaparsec, thus extending the range of sources that can be referenced to a GNSS antenna by 18 orders of magnitude. These detections represent the first observations made with a GNSS antenna to radio telescope interferometer. We have developed a novel technique based on a Precise Point Positioning (PPP) solution of the recorded GNSS signal that allows us to extend integration time at 1.5 GHz to at least 20 minutes without any noticeable SNR degradation when a rubidium frequency standard is used.

physics.geo-ph↗

arXiv2023

Rewriting History in Integrable Stochastic Particle Systems

Many integrable stochastic particle systems in one space dimension (such as TASEP - Totally Asymmetric Simple Exclusion Process - and its $q$-deformation, the $q$-TASEP) remain integrable if we equip each particle with its own speed parameter. In this work, we present intertwining relations between Markov transition operators of particle systems which differ by a permutation of the speed parameters. These relations generalize our previous works (arXiv:1907.09155, arXiv:1912.06067), but here we employ a novel approach based on the Yang-Baxter equation for the higher spin stochastic six vertex model. Our intertwiners are Markov transition operators, which leads to interesting probabilistic consequences. First, we obtain a new Lax-type differential equation for the Markov transition semigroups of homogeneous, continuous-time versions of our particle systems. Our Lax equation encodes the time evolution of multipoint observables of the $q$-TASEP and TASEP in a unified way, which may be of interest for the asymptotic analysis of multipoint observables of these systems. Second, we show that our intertwining relations lead to couplings between probability measures on trajectories of particle systems which differ by a permutation of the speed parameters. The conditional distribution for such a coupling is realized as a "rewriting history" random walk which randomly resamples the trajectory of a particle in a chamber determined by the trajectories of the neighboring particles. As a byproduct, we construct a new coupling for standard Poisson processes on the positive real half-line with different rates.

math.PR↗

arXiv2023

Asymptotics of noncolliding q-exchangeable random walks

We consider a process of noncolliding $q$-exchangeable random walks on $\mathbb{Z}$ making steps $0$ (straight) and $-1$ (down). A single random walk is called $q$-exchangeable if under an elementary transposition of the neighboring steps (down, straight) $\to$ (straight, down) the probability of the trajectory is multiplied by a parameter $q\in(0,1)$. Our process of $m$ noncolliding $q$-exchangeable random walks is obtained from the independent $q$-exchangeable walks via the Doob's $h$-transform for a certain nonnegative eigenfunction $h$ with the eigenvalue less than $1$. The system of $m$ walks evolves in the presence of an absorbing wall at $0$. We show that the trajectory of the noncolliding $q$-exchangeable walks started from an arbitrary initial configuration forms a determinantal point process, and express its kernel in a double contour integral form. This kernel is obtained as a limit from the correlation kernel of $q$-distributed random lozenge tilings of sawtooth polygons. In the limit as $m\to \infty$, $q=e^{-γ/m}$ with $γ>0$ fixed, and under a suitable scaling of the initial data, we obtain a limit shape of our noncolliding walks and also show that their local statistics are governed by the incomplete beta kernel. The latter is a distinguished translation invariant ergodic extension of the two-dimensional discrete sine kernel.

math.PR↗

arXiv2023

VGOS VLBI Intensives between MACGO12M and WETTZ13S for the rapid determination of UT1-UTC

In this work, we present a status update and results of the designated research and development VLBI Intensive program VGOS-INT-S, observed between MACGO12M and WETTZ13S for the rapid determination of the Earth's phase of rotation, expressed via UT1-UTC. The main novelty of these sessions is the use of a special observation strategy, rapidly alternating between high- and low-elevation scans, enabling an improved determination of delays caused by the neutral atmosphere. Since 2021, 25 Intensive sessions have been observed successfully. In early 2022, VGOS-INT-S was among the most accurate Intensive programs with an average formal error $σ_{UT1-UTC}$ of 3.1 $μ$s and a bias w.r.t. IERS C04 of 1.1 $μ$s. Later, the session performance decreased due to multiple technical difficulties.

physics.geo-ph↗

arXiv2023

Single band VLBI absolute astrometry

The ionospheric path delay impacts single-band very long baseline interferometry (VLBI) group delays, which limits their applicability for absolute astrometry. I consider two important cases: when observations are made simultaneously at two bands, but delays at only one band are available for a subset of observations and when observations are made at one band by design. I developed optimal procedures of data analysis for both cases using Global Navigation Satellite System (GNSS) ionosphere maps, provided a stochastic model that describes ionospheric errors, and evaluated their impact on source position estimates. I demonstrate that the stochastic model is accurate at a level of 15%. I found that using GNSS ionospheric maps as is introduces serious biases in estimates of declinations and I developed the procedure that almost eliminates them. I found serendipitously that GNSS ionospheric maps have multiplicative errors and have to be scaled by 0.85 in order to mitigate the declination bias. A similar scale factor was found in comparison of the vertical total electron contents from satellite altimetry against GNSS ionospheric maps. I favor interpretation of this scaling factor as a manifestation of the inadequacy of the thin shell model of the ionosphere. I showed that we are able to model the ionospheric path delay to the extent that no noticeable systematic errors emerge and we are able to adequately assess the contribution of the ionosphere-driven random errors on source positions. This makes single-band absolute astrometry a viable option that can be used for source position determination.

astro-ph.IM↗

arXiv2023

Precise VLBI/GNSS ties with micro-VLBI

We present here a concept of measuring local ties between collocated GNSS and VLBI stations using the microwave technique that effectively transforms a GNSS receiver to an element of a VLBI network. This is achieved by modifying the signal chain that allows to transfer voltage of the GNSS antenna to a digitizer via a coaxial cable. We discuss the application of this technique to local tie measurement. We have performed observations with a GNSS antenna and FD-VLBA radiotelescope and detected a strong interferometric signal from both radiogalaxies and GNSS satellites.

physics.geo-ph↗

arXiv2023

Free Fermion Six Vertex Model: Symmetric Functions and Random Domino Tilings

Our work deals with symmetric rational functions and probabilistic models based on the fully inhomogeneous six vertex (ice type) model satisfying the free fermion condition. Two families of symmetric rational functions $F_λ,G_λ$ are defined as certain partition functions of the six vertex model, with variables corresponding to row rapidities, and the labeling signatures $λ=(λ_1\ge \ldots\ge λ_N)\in \mathbb{Z}^N$ encoding boundary conditions. These symmetric functions generalize Schur symmetric polynomials, as well as some of their variations, such as factorial and supersymmetric Schur polynomials. Cauchy type summation identities for $F_λ,G_λ$ and their skew counterparts follow from the Yang-Baxter equation. Using algebraic Bethe Ansatz, we obtain a double alternant type formula for $F_λ$ and a Sergeev-Pragacz type formula for $G_λ$. In the spirit of the theory of Schur processes, we define probability measures on sequences of signatures with probability weights proportional to products of our symmetric functions. We show that these measures can be viewed as determinantal point processes, and we express their correlation kernels in a double contour integral form. We present two proofs: The first is a direct computation of Eynard-Mehta type, and the second uses non-standard, inhomogeneous versions of fermionic operators in a Fock space coming from the algebraic Bethe Ansatz for the six vertex model. We also interpret our determinantal processes as random domino tilings of a half-strip with inhomogeneous domino weights. In the bulk, we show that the lattice asymptotic behavior of such domino tilings is described by a new determinantal point process on $\mathbb{Z}^{2}$, which can be viewed as an doubly-inhomogeneous generalization of the extended discrete sine process.

math.PR↗

arXiv2022

Noncolliding Macdonald Walks with an Absorbing Wall

The branching rule is one of the most fundamental properties of the Macdonald symmetric polynomials. It expresses a Macdonald polynomial as a nonnegative linear combination of Macdonald polynomials with smaller number of variables. Taking a limit of the branching rule under the principal specialization when the number of variables goes to infinity, we obtain a Markov chain of $m$ noncolliding particles with negative drift and an absorbing wall at zero. The chain depends on the Macdonald parameters $(q,t)$ and may be viewed as a discrete deformation of the Dyson Brownian motion. The trajectory of the Markov chain is equivalent to a certain Gibbs ensemble of plane partitions with an arbitrary cascade front wall. In the Jack limit $t=q^{β/2}\to 1$ the absorbing wall disappears, and the Macdonald noncolliding walks turn into the $β$-noncolliding random walks studied by Huang [Int. Math. Res. Not. 2021 (2021), 5898-5942, arXiv:1708.07115]. Taking $q=0$ (Hall-Littlewood degeneration) and further sending $t\to 1$, we obtain a continuous time particle system on $\mathbb{Z}_{\ge 0}$ with inhomogeneous jump rates and absorbing wall at zero.

math.PR↗

arXiv2022

Irreversible Markov Dynamics and Hydrodynamics for KPZ States in the Stochastic Six Vertex Model

We introduce a family of Markov growth processes on discrete height functions defined on the 2-dimensional square lattice. Each height function corresponds to a configuration of the six vertex model on the infinite square lattice. We focus on the stochastic six vertex model corresponding to a particular two-parameter family of weights within the ferroelectric regime. It is believed (and partially proven, see Aggarwal, arXiv:2004.13272) that the stochastic six vertex model displays nontrivial pure (i.e., translation invariant and ergodic) Gibbs states of two types, KPZ and liquid. These phases have very different long-range correlation structure. The Markov processes we construct preserve the KPZ pure states in the full plane. We also show that the same processes put on the torus preserve arbitrary Gibbs measures for generic six vertex weights (not necessarily in the ferroelectric regime). Our dynamics arise naturally from the Yang-Baxter equation for the six vertex model via its bijectivisation, a technique first used in Bufetov-Petrov (arXiv:1712.04584). The dynamics we construct are irreversible; in particular, the height function has a nonzero average drift. In each KPZ pure state, we explicitly compute the average drift (also known as the current) as a function of the slope. We use this to analyze the hydrodynamics of a non-stationary version of our process acting on quarter plane stochastic six vertex configurations. The fixed-time limit shapes in the quarter plane model were obtained in Borodin-Corwin-Gorin (arXiv:1407.6729).

math.PR↗

arXiv2021

Parameter symmetry in perturbed GUE corners process and reflected drifted Brownian motions

The perturbed GUE corners ensemble is the joint distribution of eigenvalues of all principal submatrices of a matrix $G+\mathrm{diag}(\mathbf{a})$, where $G$ is the random matrix from the Gaussian Unitary Ensemble (GUE), and $\mathrm{diag}(\mathbf{a})$ is a fixed diagonal matrix. We introduce Markov transitions based on exponential jumps of eigenvalues, and show that their successive application is equivalent in distribution to a deterministic shift of the matrix. This result also leads to a new distributional symmetry for a family of reflected Brownian motions with drifts coming from an arithmetic progression. The construction we present may be viewed as a random matrix analogue of the recent results of the first author and Axel Saenz (arXiv:1907.09155 [math.PR]).

math.PR↗

arXiv2021

Refined Cauchy identity for spin Hall-Littlewood symmetric rational functions

Fully inhomogeneous spin Hall-Littlewood symmetric rational functions $\mathsf{F}_λ$ arise in the context of $\mathfrak{sl}(2)$ higher spin six vertex models, and are multiparameter deformations of the classical Hall-Littlewood symmetric polynomials. We obtain a refined Cauchy identity expressing a weighted sum of the product of two $\mathsf{F}_λ$'s as a determinant. The determinant is of Izergin-Korepin type: it is the partition function of the six vertex model with suitably decorated domain wall boundary conditions. The proof of equality of two partition functions is based on the Yang-Baxter equation. We rewrite our Izergin-Korepin type determinant in a different form which includes one of the sets of variables in a completely symmetric way. This determinantal identity might be of independent interest, and also allows to directly link the spin Hall-Littlewood rational functions with (the Hall-Littlewood particular case of) the interpolation Macdonald polynomials. In a different direction, a Schur expansion of our Izergin-Korepin type determinant yields a deformation of Schur symmetric polynomials. In the spin-$\frac12$ specialization, our refined Cauchy identity leads to a summation identity for eigenfunctions of the ASEP (Asymmetric Simple Exclusion Process), a celebrated stochastic interacting particle system in the Kardar-Parisi-Zhang universality class. This produces explicit integral formulas for certain multitime probabilities in ASEP.

math.CO↗

arXiv2021

The use of astronomy VLBA campaign MOJAVE for geodesy

We investigated the suitability of the astronomical 15 GHz VLBA observing program MOJAVE-5 for estimation of geodetic parameters, such as station coordinates and Earth orientation parameters. We processed contemporary geodetic dual-band RV and CN experiments observed at 2.3 GHz and 8.6 GHz starting on September 2016 through July 2020 as reference dataset. We showed that the baseline length repeatability from MOJAVE-5 experiments is only a factor of 1.5 greater than from the dedicated geodetic dataset and still below 1~ppb. The wrms of the difference of estimated EOP with respect to the reference IERS C04 time series are a factor of 1.3 to 1.8 worse. We isolated three major differences between the datasets in terms their possible impact on the geodetic results, i.e. the scheduling approach, treatment of the ionospheric delay, and selection of target radio sources. We showed that the major factor causing discrepancies in the estimated geodetic parameters is the different scheduling approach of the datasets. We conclude that systematic errors in MOJAVE-5 dataset are low enough for these data to be used as an excellent testbed for further investigations on the radio source structure effects in geodesy and astrometry.

astro-ph.IM↗

arXiv2021

Parameter Permutation Symmetry in Particle Systems and Random Polymers

Many integrable stochastic particle systems in one space dimension (such as TASEP - totally asymmetric simple exclusion process - and its various deformations, with a notable exception of ASEP) remain integrable when we equip each particle $x_i$ with its own jump rate parameter $ν_i$. It is a consequence of integrability that the distribution of each particle $x_n(t)$ in a system started from the step initial configuration depends on the parameters $ν_j$, $j\le n$, in a symmetric way. A transposition $ν_n \leftrightarrow ν_{n+1}$ of the parameters thus affects only the distribution of $x_n(t)$. For $q$-Hahn TASEP and its degenerations ($q$-TASEP and directed beta polymer) we realize the transposition $ν_n \leftrightarrow ν_{n+1}$ as an explicit Markov swap operator acting on the single particle $x_n(t)$. For beta polymer, the swap operator can be interpreted as a simple modification of the lattice on which the polymer is considered. Our main tools are Markov duality and contour integral formulas for joint moments. In particular, our constructions lead to a continuous time Markov process $\mathsf{Q}^{(\mathsf{t})}$ preserving the time $\mathsf{t}$ distribution of the $q$-TASEP (with step initial configuration, where $\mathsf{t}\in \mathbb{R}_{>0}$ is fixed). The dual system is a certain transient modification of the stochastic $q$-Boson system. We identify asymptotic survival probabilities of this transient process with $q$-moments of the $q$-TASEP, and use this to show the convergence of the process $\mathsf{Q}^{(\mathsf{t})}$ with arbitrary initial data to its stationary distribution. Setting $q=0$, we recover the results about the usual TASEP established recently in [arXiv:1907.09155] by a different approach based on Gibbs ensembles of interlacing particles in two dimensions.

math.PR↗

arXiv2021

A ring accelerator? Unusual jet dynamics in the IceCube candidate PKS 1502+106

On 2019/07/30.86853 UT, IceCube detected a high-energy astrophysical neutrino candidate. The Flat Spectrum Radio Quasar PKS 1502+106 is located within the 50 percent uncertainty region of the event. Our analysis of 15 GHz Very Long Baseline Array (VLBA) and astrometric 8 GHz VLBA data, in a time span prior and after the IceCube event, reveals evidence for a radio ring structure which develops with time. Several arc-structures evolve perpendicular to the jet ridge line. We find evidence for precession of a curved jet based on kinematic modelling and a periodicity analysis. An outflowing broad line region (BLR) based on the C IV line emission (Sloan Digital Sky Survey, SDSS) is found. We attribute the atypical ring to an interaction of the precessing jet with the outflowing material. We discuss our findings in the context of a spine-sheath scenario where the ring reveals the sheath and its interaction with the surroundings (narrow line region, NLR, clouds). We find that the radio emission is correlated with the $γ$-ray emission, with radio lagging the $γ$-rays. Based on the $γ$-ray variability timescale, we constrain the $γ$-ray emission zone to the BLR (30-200 $r_{\rm g}$) and within the jet launching region. We discuss that the outflowing BLR provides the external radiation field for $γ$-ray production via external Compton scattering. The neutrino is most likely produced by proton-proton interaction in the blazar zone (beyond the BLR), enabled by episodic encounters of the jet with dense clouds, i.e. some molecular cloud in the NLR.

astro-ph.HE↗

arXiv2021

Mapping TASEP back in time

We obtain a new relation between the distributions $μ_t$ at different times $t\ge 0$ of the continuous-time TASEP (Totally Asymmetric Simple Exclusion Process) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions $μ_t$ backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving $μ_t$ which in turn brings new identities for expectations with respect to $μ_t$. The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang-Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.

math.PR↗

arXiv2020

Quasars That Have Transitioned from Radio-quiet to Radio-loud on Decadal Timescales Revealed by VLASS and FIRST

We have performed a search over 3440 deg$^2$ of Epoch 1 (2017-2019) of the Very Large Array Sky Survey to identify unobscured quasars in the optical ($0.2 < z < 3.2$) and obscured active galactic nuclei (AGN) in the infrared that have brightened dramatically in the radio over the past one to two decades. These sources would have been previously classified as "radio-quiet" quasars based on upper limits from the Faint Images of the Radio Sky at Twenty Centimeters survey (1993-2011), but they are now consistent with "radio-loud" quasars ($L_{\rm 3\,GHz} = 10^{40 - 42} \,\, {\rm erg} \,{\rm s}^{-1}$). A quasi-simultaneous, multiband ($\sim1-18$ GHz) follow-up study of 14 sources with the VLA has revealed compact sources ($<0.1^{\prime \prime}$ or $<1$ kpc) with peaked radio spectral shapes. The high-amplitude variability over decadal timescales at 1.5 GHz (100% to $>$2500%), but roughly steady fluxes over a few months at 3 GHz, are inconsistent with extrinsic variability due to propagation effects, thus favoring an intrinsic origin. We conclude that our sources are powerful quasars hosting compact/young jets. This challenges the generally accepted idea that "radio-loudness" is a property of the quasar/AGN population that remains fixed on human timescales. Our study suggests that frequent episodes of short-lived AGN jets that do not necessarily grow to large scales may be common at high redshift. We speculate that intermittent but powerful jets on subgalactic scales could interact with the interstellar medium, possibly driving feedback capable of influencing galaxy evolution.

astro-ph.GA↗