arXiv subjects

Leonid Petrov

Publications and source records attributed to Leonid Petrov.

At least 55 records · Page 3Linked to original sources

arXiv2020

The wide-field VLBA calibrator survey -- WFCS

The paper presents the results of the largest to date VLBI absolute astrometry campaign of observations of 13,645 radio sources with the Very Long Baseline Array (VLBA). Of them, 7220 have been detected, including 6755 target sources that have never been observed with VLBI before. This makes the present VLBI catalogue the largest ever published. Positions of the target sources have been determined with the median uncertainty 1.7 mas, and 15,599 images of 7179 sources have been generated. Unlike to previous absolute radio astrometry campaigns, observations were made at 4.3 and 7.6 GHz simultaneously using a single wide-band receiver. Because of the fine spectral and time resolutions, the field of view was 4 to 8 arcminutes -- much greater than 10 to 20 arcseconds in previous surveys. This made possible to use input catalogues with low position accuracy and detect a compact component in extended sources. Unlike to previous absolute astrometry campaigns, both steep and flat spectrum sources were observed. The observations were scheduled in the so-called fill-in mode to fill the gaps between other high priority programs. That was achieved by development of the totally automatic scheduling procedure.

astro-ph.IM↗

arXiv2020

VLBI20-30: a scientific roadmap for the next decade -- The future of the European VLBI Network

This white paper describes the science case for Very Long Baseline Interferometry (VLBI) and provides suggestions towards upgrade paths for the European VLBI Network (EVN). The EVN is a distributed long-baseline radio interferometric array, that operates at the very forefront of astronomical research. Recent results, together with the new science possibilities outlined in this vision document, demonstrate the EVN's potential to generate new and exciting results that will transform our view of the cosmos. Together with e-MERLIN, the EVN provides a range of baseline lengths that permit unique studies of faint radio sources to be made over a wide range of spatial scales. The science cases are reviewed in six chapters that cover the following broad areas: cosmology, galaxy formation and evolution, innermost regions of active galactic nuclei, explosive phenomena and transients, stars and stellar masers in the Milky Way, celestial reference frames and space applications. The document concludes with identifying the synergies with other radio, as well as multi-band/multi-messenger instruments, and provide the recommendations for future improvements. The appendices briefly describe other radio VLBI arrays, the technological framework for EVN developments, and a selection of spectral lines of astrophysical interest below 100 GHz. The document includes a glossary for non-specialists, and a list of acronyms at the end.

astro-ph.IM↗

arXiv2020

Influence of the Galactic gravitational field on the positional accuracy of extragalactic sources. II Observational appearances and detectability

We consider a possibility of detecting the jitter effect of apparent celestial positions of distant sources due to local fluctuations of the Galaxy gravitational field. It is proposed to observe two samples of extragalactic sources (target and control) in different sky directions using the high-precision radio interferometry. It is shown that on a scale of ~2 years, it is possible to detect a systematic increase in the standard deviation of measured arc lengths of pairs of target sources compared to the control ones at the $3σ$-level if the accuracy of differential astrometric observations is around 10 $μ$as. For the current state-of-the-art accuracy of 30 $μ$as achieved at the KVN or VERA interferometers, which have shorter baselines in comparison with VLBI, the target and control samples will differ only at the 2$σ$-level on the scale of 10 years. To achieve the $3σ$-level on this time interval, it is necessary to improve the accuracy up to ~20 $μ$as. Other possible effects that can also affect the arc length measurements between two sources are discussed, and an observational strategy to minimize them is suggested.

astro-ph.GA↗

arXiv2020

PushTASEP in inhomogeneous space

We consider the PushTASEP (pushing totally asymmetric simple exclusion process, also sometimes called long-range TASEP) with the step initial configuration evolving in an inhomogeneous space. That is, the rate of each particle's jump depends on the location of this particle. We match the distribution of the height function of this PushTASEP with Schur processes. Using this matching and determinantal structure of Schur processes, we obtain limit shape and fluctuation results which are typical for stochastic particle systems in the Kardar-Parisi-Zhang universality class. PushTASEP is a close relative of the usual TASEP. In inhomogeneous space the former is integrable, while the integrability of the latter is not known.

math.PR↗

arXiv2020

Spin q-Whittaker polynomials and deformed quantum Toda

Spin $q$-Whittaker symmetric polynomials labeled by partitions $λ$ were recently introduced by Borodin and Wheeler (arXiv:1701.06292) in the context of integrable $\mathfrak{sl}_2$ vertex models. They are a one-parameter deformation of the $t=0$ Macdonald polynomials. We present a new, more convenient modification of spin $q$-Whittaker polynomials and find two Macdonald type $q$-difference operators acting diagonally in these polynomials with eigenvalues, respectively, $q^{-λ_1}$ and $q^{λ_N}$ (where $λ$ is the polynomial's label). We study probability measures on interlacing arrays based on spin $q$-Whittaker polynomials, and match their observables with known stochastic particle systems such as the $q$-Hahn TASEP. In a scaling limit as $q\nearrow 1$, spin $q$-Whittaker polynomials turn into a new one-parameter deformation of the $\mathfrak{gl}_n$ Whittaker functions. The rescaled Pieri type rule gives rise to a one-parameter deformation of the quantum Toda Hamiltonian. The deformed Hamiltonian acts diagonally on our new spin Whittaker functions. On the stochastic side, as $q\nearrow 1$ we discover a multilevel extension of the beta polymer model of Barraquand and Corwin (arXiv:1503.04117), and relate it to spin Whittaker functions.

math.PR↗

arXiv2019

Yang-Baxter random fields and stochastic vertex models

Bijectivization refines the Yang-Baxter equation into a pair of local Markov moves which randomly update the configuration of the vertex model. Employing this approach, we introduce new Yang-Baxter random fields of Young diagrams based on spin $q$-Whittaker and spin Hall-Littlewood symmetric functions. We match certain scalar Markovian marginals of these fields with (1) the stochastic six vertex model; (2) the stochastic higher spin six vertex model; and (3) a new vertex model with pushing which generalizes the $q$-Hahn PushTASEP introduced recently by Corwin-Matveev-Petrov (arXiv:1811.06475). Our matchings include models with two-sided stationary initial data, and we obtain Fredholm determinantal expressions for the $q$-Laplace transforms of the height functions of all these models. Moreover, we also discover difference operators acting diagonally on spin $q$-Whittaker or (stable) spin Hall-Littlewood symmetric functions.

math.PR↗

arXiv2019

Stochastic higher spin vertex models on the line

We introduce a four-parameter family of interacting particle systems on the line which can be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which enjoy certain Markov dualities. Using this, for the systems started in step initial data we write down nested contour integral formulas for moments and Fredholm determinant formulas for Laplace-type transforms. Taking various choices or limits of parameters, this family degenerates to many of the known exactly solvable models in the Kardar-Parisi-Zhang universality class, as well as leads to many new examples of such models. In particular, ASEP, the stochastic six-vertex model, q-TASEP and various directed polymer models all arise in this manner. Our systems are constructed from stochastic versions of the R-matrix related to the six-vertex model. One of the key tools used here is the fusion of R-matrices and we provide a probabilistic proof of this procedure.

math.PR↗

arXiv2019

The q-Hahn PushTASEP

We introduce the $q$-Hahn PushTASEP --- an integrable stochastic interacting particle system which is a 3-parameter generalization of the PushTASEP, a well-known close relative of the TASEP (Totally Asymmetric Simple Exclusion Process). The transition probabilities in the $q$-Hahn PushTASEP are expressed through the $_4ϕ_3$ basic hypergeometric function. Under suitable limits, the $q$-Hahn PushTASEP degenerates to all known integrable (1+1)-dimensional stochastic systems with a pushing mechanism. One can thus view our new system as a pushing counterpart of the $q$-Hahn TASEP introduced by Povolotsky (2013). We establish Markov duality relations and contour integral formulas for the $q$-Hahn PushTASEP. In a $q\to 1$ limit of our process we arrive at a random recursion which, in a special case, appears to be similar to the inverse-Beta polymer model. However, unlike in recursions for Beta polymer models, the weights (i.e., the coefficients of the recursion) in our model depend on the previous values of the partition function in a nontrivial manner.

math.PR↗

arXiv2019

Generalizations of TASEP in discrete and continuous inhomogeneous space

We investigate a rich new class of exactly solvable particle systems generalizing the Totally Asymmetric Simple Exclusion Process (TASEP). Our particle systems can be thought of as new exactly solvable examples of tandem queues, directed first- or last-passage percolation models, or Robinson-Schensted-Knuth type systems with random input. One of the novel features of the particle systems is the presence of spatial inhomogeneity which can lead to the formation of traffic jams. For systems with special step-like initial data, we find explicit limit shapes, describe hydrodynamic evolution, and obtain asymptotic fluctuation results which put the systems into the Kardar-Parisi-Zhang universality class. At a critical scaling around a traffic jam in the continuous space TASEP, we observe deformations of the Tracy-Widom distribution and the extended Airy kernel, revealing the finer structure of this novel type of phase transitions. A homogeneous version of a discrete space system we consider is a one-parameter deformation of the geometric last-passage percolation, and we obtain extensions of the limit shape parabola and the corresponding asymptotic fluctuation results. The exact solvability and asymptotic behavior results are powered by a new nontrivial connection to Schur measures and processes.

math.PR↗

arXiv2019

The Second LBA Calibrator Survey of southern compact extragalactic radio sources - LCS2

We present the second catalogue of accurate positions and correlated flux densities for 1100 compact extragalactic radio sources that were not observed before 2008 at high angular resolution. The catalogue spans the declination range -90 deg, -30 deg and was constructed from nineteen 24-hour VLBI observing sessions with the Australian Long Baseline Array at 8.3 GHz. The catalogue presents the final part of the program that was started in 2008. The goals of that campaign were 1) to extend the number of compact radio sources with precise coordinates and measure their correlated flux densities, which can be used for phase referencing VLBI and ALMA observations, geodetic VLBI, search for sources with significant offsets with respect to Gaia positions, and space navigation; 2) to extend the complete flux-limited sample of compact extragalactic sources to the Southern Hemisphere; and 3) to investigate the parsec-scale properties of sources from the high-frequency AT20G survey. The median uncertainty of the source positions is 3.5 mas. As a result of this VLBI campaign, the number of compact radio sources south of declination -40 deg which have measured VLBI correlated flux densities and positions known to milliarcsecond accuracy has increased by over a factor of 6.

astro-ph.IM↗

arXiv2019

The Next Generation Celestial Reference Frame

Astrometry, the measurement of positions and motions of the stars, is one of the oldest disciplines in Astronomy, extending back at least as far as Hipparchus' discovery of the precession of Earth's axes in 190 BCE by comparing his catalog with those of his predecessors. Astrometry is fundamental to Astronomy, and critical to many aspects of Astrophysics and Geodesy. In order to understand our planet's and solar system's context within their surroundings, we must be able to to define, quantify, study, refine, and maintain an inertial frame of reference relative to which all positions and motions can be unambiguously and self-consistently described. It is only by using this inertial reference frame that we are able to disentangle our observations of the motions of celestial objects from our own complex path around our star, and its path through the galaxy, and the local group. Every aspect of each area outlined in the call for scientific frontiers in astronomy in the era of the 2020-2030 timeframe will depend on the quality of the inertial reference frame. In this white paper, we propose support for development of radio Very Long Baseline Interferometry (VLBI) capabilities, including the Next Generation Very Large Array (ngVLA), a radio astronomy observatory that will not only support development of a next generation reference frame of unprecedented accuracy, but that will also serve as a highly capable astronomical instrument in its own right. Much like its predecessors, the Very Long Baseline Array (VLBA) and other VLBI telescopes, the proposed ngVLA will provide the foundation for the next three decades for the fundamental reference frame, benefitting astronomy, astrophysics, and geodesy alike.

astro-ph.IM↗

arXiv2018

Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz

We develop spectral theory for the q-Hahn stochastic particle system introduced recently by Povolotsky. That is, we establish a Plancherel type isomorphism result which implies completeness and biorthogonality statements for the Bethe ansatz eigenfunctions of the system. Owing to a Markov duality with the q-Hahn TASEP (a discrete-time generalization of TASEP with particles' jump distribution being the orthogonality weight for the classical q-Hahn orthogonal polynomials), we write down moment formulas which characterize the fixed time distribution of the q-Hahn TASEP with general initial data. The Bethe ansatz eigenfunctions of the q-Hahn system degenerate into eigenfunctions of other (not necessarily stochastic) interacting particle systems solvable by the coordinate Bethe ansatz. This includes the ASEP, the (asymmetric) six-vertex model, and the Heisenberg XXZ spin chain (all models are on the infinite lattice). In this way, each of the latter systems possesses a spectral theory, too. In particular, biorthogonality of the ASEP eigenfunctions which follows from the corresponding q-Hahn statement implies symmetrization identities of Tracy and Widom (for ASEP with either step or step Bernoulli initial configuration) as corollaries. Another degeneration takes the q-Hahn system to the q-Boson particle system (dual to q-TASEP) studied in detail in our previous paper (2013). Thus, at the spectral theory level we unify two discrete-space regularizations of the Kardar-Parisi-Zhang equation / stochastic heat equation, namely, q-TASEP and ASEP.

math-ph↗

arXiv2018

Quenched Central Limit Theorem in a Corner Growth Setting

We consider point-to-point directed paths in a random environment on the two-dimensional integer lattice. For a general independent environment under mild assumptions we show that the quenched energy of a typical path satisfies a central limit theorem as the mesh of the lattice goes to zero. Our proofs rely on concentration of measure techniques and some combinatorial bounds on families of paths.

math.PR↗

arXiv2018

Radio interferometric observation of an asteroid occultation

The occultation of the radio galaxy 0141+268 by the asteroid (372) Palma on 2017 May 15 was observed using six antennas of the Very Long Baseline Array (VLBA). The shadow of Palma crossed the VLBA station at Brewster, Washington. Owing to the wavelength used, and the size and the distance of the asteroid, a diffraction pattern in the Fraunhofer regime was observed. The measurement retrieves both the amplitude and the phase of the diffracted electromagnetic wave. This is the first astronomical measurement of the phase shift caused by diffraction. The maximum phase shift is sensitive to the effective diameter of the asteroid. The bright spot at the shadow's center, the so called Arago--Poisson spot, is clearly detected in the amplitude time-series, and its strength is a good indicator of the closest angular distance between the center of the asteroid and the radio source. A sample of random shapes constructed using a Markov chain Monte Carlo algorithm suggests that the silhouette of Palma deviates from a perfect circle by 26+-13%. The best-fitting random shapes resemble each other, and we suggest their average approximates the shape of the silhouette at the time of the occultation. The effective diameter obtained for Palma, 192.1+-4.8 km, is in excellent agreement with recent estimates from thermal modeling of mid-infrared photometry. Finally, our computations show that because of the high positional accuracy, a single radio interferometric occultation measurement can reduce the long-term ephemeris uncertainty by an order of magnitude.

astro-ph.EP↗

arXiv2018

Universality of local statistics for noncolliding random walks

We consider the $N$-particle noncolliding Bernoulli random walk --- a discrete time Markov process in $\mathbb{Z}^{N}$ obtained from a collection of $N$ independent simple random walks with steps $\in\{0,1\}$ by conditioning that they never collide. We study the asymptotic behavior of local statistics of this process started from an arbitrary initial configuration on short times $T\ll N$ as $N\to+\infty$. We show that if the particle density of the initial configuration is bounded away from $0$ and $1$ down to scales $\mathsf{D}\ll T$ in a neighborhood of size $\mathsf{Q}\gg T$ of some location $x$ (i.e., $x$ is in the "bulk"), and the initial configuration is balanced in a certain sense, then the space-time local statistics at $x$ are asymptotically governed by the extended discrete sine process (which can be identified with a translation invariant ergodic Gibbs measure on lozenge tilings of the plane). We also establish similar results for certain types of random initial data. Our proofs are based on a detailed analysis of the determinantal correlation kernel for the noncolliding Bernoulli random walk. The noncolliding Bernoulli random walk is a discrete analogue of the $β=2$ Dyson Brownian Motion whose local statistics are universality governed by the continuous sine process. Our results parallel the ones in the continuous case. In addition, we naturally include situations with inhomogeneous local particle density on scale $T$, which nontrivially affects parameters of the limiting extended sine process, and in a particular case leads to a new behavior.

math.PR↗

arXiv2018

Coarsening model on $\mathbb{Z}^d$ with biased zero-energy flips and an exponential large deviation bound for ASEP

We study the coarsening model (zero-temperature Ising Glauber dynamics) on $\mathbb{Z}^d$ (for $d \geq 2$) with an asymmetric tie-breaking rule. This is a Markov process on the state space $\{-1,+1\}^{\mathbb{Z}^d}$ of "spin configurations" in which each vertex updates its spin to agree with a majority of its neighbors at the arrival times of a Poisson process. If a vertex has equally many $+1$ and $-1$ neighbors, then it updates its spin value to $+1$ with probability $q \in [0,1]$ and to $-1$ with probability $1-q$. The initial state of this Markov chain is distributed according to a product measure with probability $p$ for a spin to be $+1$. In this paper, we show that for any given $p>0$, there exist $q$ close enough to 1 such that a.s. every spin has a limit of $+1$. This is of particular interest for small values of $p$, for which it is known that if $q=1/2$, a.s. all spins have a limit of $-1$. For dimension $d=2$, we also obtain near-exponential convergence rates for $q$ sufficiently large, and for general $d$, we obtain stretched exponential rates independent of $d$. Two important ingredients in our proofs are refinements of block arguments of Fontes-Schonmann-Sidoravicius and a novel exponential large deviation bound for the Asymmetric Simple Exclusion Process.

math.PR↗

arXiv2018

Yang-Baxter field for spin Hall-Littlewood symmetric functions

Employing bijectivisation of summation identities, we introduce local stochastic moves based on the Yang-Baxter equation for $U_q(\widehat{\mathfrak{sl}_2})$. Combining these moves leads to a new object which we call the spin Hall-Littlewood Yang-Baxter field - a probability distribution on two-dimensional arrays of particle configurations on the discrete line. We identify joint distributions along down-right paths in the Yang-Baxter field with spin Hall-Littlewood processes, a generalization of Schur processes. We consider various degenerations of the Yang-Baxter field leading to new dynamic versions of the stochastic six vertex model and of the Asymmetric Simple Exclusion Process.

math.PR↗

arXiv2017

Observational consequences of optical band milliarcsecond-scale structure in active galactic nuclei discovered by Gaia

We interpret the recent discovery of a preferable VLBI/Gaia offset direction for radio-loud active galactic nuclei (AGNs) along the parsec-scale radio jets as a manifestation of their optical structure on scales of 1 to 100 milliarcseconds. The extended jet structure affects the Gaia position stronger than the VLBI position due to the difference in observing techniques. Gaia detects total power while VLBI measures the correlated quantity, visibility, and therefore, sensitive to compact structures. The synergy of VLBI that is sensitive to the position of the most compact source component, usually associated with the opaque radio core, and Gaia that is sensitive to the centroid of optical emission, opens a window of opportunity to study optical jets at milliarcsecond resolution, two orders of magnitude finer than the resolution of most existing optical instruments. We demonstrate that strong variability of optical jets is able to cause a jitter comparable to the VLBI/Gaia offsets at a quiet state, i.e. several milliarcseconds. We show that the VLBI/Gaia position jitter correlation with the AGN optical light curve may help to locate the region where the flare occurred, estimate its distance from the super-massive black hole and the ratio of the flux density in the flaring region to the total flux density.

astro-ph.HE↗