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Leonid Petrov

Publications and source records attributed to Leonid Petrov.

At least 73 records · Page 4Linked to original sources
arXiv2017

VLBI ecliptic plane survey: VEPS-1

We present here the results of the first part of the VLBI Ecliptic Plane Survey (VEPS) program. The goal of the program is to find all compact sources within $7.5^\circ$ of the ecliptic plane which are suitable as calibrators for anticipated phase referencing observations of spacecraft and determine their positions with accuracy at the 1.5~nrad level. We run the program in two modes: the search mode and the refining mode. In the search mode, a complete sample of all sources brighter than 50 mJy at 5 GHz listed in the Parkes-MIT-NRAO (PMN) and Green Bank 6~cm (GB6) catalogs, except those previously detected with VLBI, is observed. In the refining mode, the positions of all ecliptic plane sources, including those found in the search mode, are improved. By October 2016, thirteen 24-hr sessions that targeted all sources brighter than 100~mJy have been observed and analyzed. Among 3320 observed target sources, 555 objects have been detected. We also conducted a number of follow-up VLBI experiments in the refining mode and improved the positions of 249 ecliptic plane sources.

astro-ph.IM↗
arXiv2017

Integrable probability: From representation theory to Macdonald processes

These are lecture notes for a mini-course given at the Cornell Probability Summer School in July 2013. Topics include lozenge tilings of polygons and their representation theoretic interpretation, the (q,t)-deformation of those leading to the Macdonald processes, nearest neighbor dynamics on Macdonald processes, their limit to semi-discrete Brownian polymers, and large time asymptotic analysis of polymer's partition function.

math.PR↗
arXiv2017

GUE corners limit of q-distributed lozenge tilings

We study asymptotics of $q$-distributed random lozenge tilings of sawtooth domains (equivalently, of random interlacing integer arrays with fixed top row). Under the distribution we consider each tiling is weighted proportionally to $q^{\mathsf{vol}}$, where $\mathsf{vol}$ is the volume under the corresponding 3D stepped surface. We prove the following Interlacing Central Limit Theorem: as $q\rightarrow1$, the domain gets large, and the fixed top row approximates a given nonrandom profile, the vertical lozenges are distributed as the eigenvalues of a GUE random matrix and of its successive principal corners. Our results extend the GUE corners asymptotics for tilings of bounded polygonal domains previously known in the uniform (i.e., $q=1$) case. Even though $q$ goes to $1$, the presence of the $q$-weighting affects non-universal constants in our Central Limit Theorem.

math.PR↗
arXiv2017

Inhomogeneous exponential jump model

We introduce and study the inhomogeneous exponential jump model - an integrable stochastic interacting particle system on the continuous half line evolving in continuous time. An important feature of the system is the presence of arbitrary spatial inhomogeneity on the half line which does not break the integrability. We completely characterize the macroscopic limit shape and asymptotic fluctuations of the height function (= integrated current) in the model. In particular, we explain how the presence of inhomogeneity may lead to macroscopic phase transitions in the limit shape such as shocks or traffic jams. Away from these singularities the asymptotic fluctuations of the height function around its macroscopic limit shape are governed by the GUE Tracy-Widom distribution. A surprising result is that while the limit shape is discontinuous at a traffic jam caused by a macroscopic slowdown in the inhomogeneity, fluctuations on both sides of such a traffic jam still have the GUE Tracy-Widom distribution (but with different non-universal normalizations). The integrability of the model comes from the fact that it is a degeneration of the inhomogeneous stochastic higher spin six vertex models studied earlier in arXiv:1601.05770 [math.PR]. Our results on fluctuations are obtained via an asymptotic analysis of Fredholm determinantal formulas arising from contour integral expressions for the q-moments in the stochastic higher spin six vertex model. We also discuss "product-form" translation invariant stationary distributions of the exponential jump model which lead to an alternative hydrodynamic-type heuristic derivation of the macroscopic limit shape.

math.PR↗
arXiv2017

Progress on VLBI Ecliptic Plane Survey

We launched the VLBI Ecliptic Plane Survey program in 2015. The goal of this program is to find all compact sources within 7.5 degrees of the ecliptic plane which are suitable as phase calibrators for anticipated phase referencing observations of spacecrafts. We planned to observe a complete sample of the sources brighter than 50 mJy at 5 GHz listed in the PMN and GB6 catalogues that have not yet been observed with VLBI. By April 2016, eight 24-hour sessions have been performed and processed. Among 2227 observed sources, 435 sources were detected in three or more observations. We have also run three 8-hour segments with VLBA for improving positions of 71 ecliptic sources.

astro-ph.IM↗
arXiv2016

Stochastic higher spin six vertex model and q-TASEPs

We present two new connections between the inhomogeneous stochastic higher spin six vertex model in a quadrant and integrable stochastic systems from the Macdonald processes hierarchy. First, we show how Macdonald $q$-difference operators with $t=0$ (an algebraic tool crucial for studying the corresponding Macdonald processes) can be utilized to get $q$-moments of the height function $\mathfrak{h}$ in the higher spin six vertex model first computed in arXiv:1601.05770 using Bethe ansatz. This result in particular implies that for the vertex model with the step Bernoulli boundary condition, the value of $\mathfrak{h}$ at an arbitrary point $(N+1,T)\in\mathbb{Z}_{\ge2}\times\mathbb{Z}_{\ge1}$ has the same distribution as the last component $λ_N$ of a random partition under a specific $t=0$ Macdonald measure. On the other hand, it is known that $\mathbf{x}_N:=λ_N-N$ can be identified with the location of the $N$th particle in a certain discrete time $q$-TASEP started from the step initial configuration. The second construction we present is a coupling of this $q$-TASEP and the higher spin six vertex model (with the step Bernoulli boundary condition) along time-like paths providing an independent probabilistic explanation of the equality of $\mathfrak{h}(N+1,T)$ and $\mathbf{x}_N+N$ in distribution. Combined with the identification of averages of observables between the stochastic higher spin six vertex model and Schur measures (which are $t=q$ Macdonald measures) obtained recently in arXiv:1608.01553, this produces GUE Tracy--Widom asymptotics for a discrete time $q$-TASEP with the step initial configuration and special jump parameters.

math.PR↗
arXiv2016

q-randomized Robinson-Schensted-Knuth correspondences and random polymers

We introduce and study q-randomized Robinson-Schensted-Knuth (RSK) correspondences which interpolate between the classical (q=0) and geometric (q->1) RSK correspondences (the latter ones are sometimes also called tropical). For 0 1, two of our four dynamics on interlacing arrays turn into the geometric RSK correspondences associated with log-Gamma or strict-weak directed random polymers.

math.PR↗
arXiv2016

Lectures on Integrable probability: Stochastic vertex models and symmetric functions

We consider a homogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations for multi-point q-moments of the height function and for the q-correlation functions. At least in the case of the step initial condition, our formulas degenerate in appropriate limits to many known formulas of such type for integrable probabilistic systems in the (1+1)d KPZ universality class, including the stochastic six vertex model, ASEP, various q-TASEPs, and associated zero range processes. Our arguments are largely based on properties of a family of symmetric rational functions (introduced in arXiv:1410.0976) that can be defined as partition functions of the higher spin six vertex model for suitable domains; they generalize classical Hall-Littlewood and Schur polynomials. A key role is played by Cauchy-like summation identities for these functions, which are obtained as a direct corollary of the Yang-Baxter equation for the higher spin six vertex model. These are lecture notes for a course given by A.B. at the Ecole de Physique des Houches in July of 2015. All the results and proofs presented here generalize to the setting of the fully inhomogeneous higher spin six vertex model, see arXiv:1601.05770 for a detailed exposition of the inhomogeneous case.

math.PR↗
arXiv2016

Higher spin six vertex model and symmetric rational functions

We consider a fully inhomogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations for multi-point q-moments of the height function and for the q-correlation functions. At least in the case of the step initial condition, our formulas degenerate in appropriate limits to many known formulas of such type for integrable probabilistic systems in the (1+1)d KPZ universality class, including the stochastic six vertex model, ASEP, various q-TASEPs, and associated zero range processes. Our arguments are largely based on properties of a family of symmetric rational functions which can be defined as partition functions of the inhomogeneous higher spin six vertex model for suitable domains. In the homogeneous case, such functions were previously studied in http://arxiv.org/abs/1410.0976; they also generalize classical Hall-Littlewood and Schur polynomials. A key role is played by Cauchy-like summation identities for these functions, which are obtained as a direct corollary of the Yang-Baxter equation for the higher spin six vertex model.

math.PR↗
arXiv2015

First scientific VLBI observations using New Zealand 30 metre radio telescope WARK30M

We report the results of a successful 24 hour 6.7 GHz VLBI experiment using the 30 meter radio telescope WARK30M near Warkworth, New Zealand, recently converted from a radio telecommunications antenna, and two radio telescopes located in Australia: Hobart 26-m and Ceduna 30-m. The geocentric position of WARK30M is determined with a 100 mm uncertainty for the vertical component and 10 mm for the horizontal components. We report correlated flux densities at 6.7 GHz of 175 radio sources associated with Fermi gamma-ray sources. A parsec scale emission from the radio source 1031-837 is detected, and its association with the gamma-ray object 2FGL J1032.9-8401 is established with a high likelihood ratio. We conclude that the new Pacific area radio telescope WARK30M is ready to operate for scientific projects.

astro-ph.IM↗
arXiv2015

1FGL J1417.7-4407: A likely gamma-ray bright binary with a massive neutron star and a giant secondary

We present multiwavelength observations of the persistent Fermi-LAT unidentified gamma-ray source 1FGL J1417.7-4407, showing it is likely to be associated with a newly discovered X-ray binary containing a massive neutron star (nearly 2 M_sun) and a ~ 0.35 M_sun giant secondary with a 5.4 day period. SOAR optical spectroscopy at a range of orbital phases reveals variable double-peaked H-alpha emission, consistent with the presence of an accretion disk. The lack of radio emission and evidence for a disk suggests the gamma-ray emission is unlikely to originate in a pulsar magnetosphere, but could instead be associated with a pulsar wind, relativistic jet, or could be due to synchrotron self-Compton at the disk--magnetosphere boundary. Assuming a wind or jet, the high ratio of gamma-ray to X-ray luminosity (~ 20) suggests efficient production of gamma-rays, perhaps due to the giant companion. The system appears to be a low-mass X-ray binary that has not yet completed the pulsar recycling process. This system is a good candidate to monitor for a future transition between accretion-powered and rotational-powered states, but in the context of a giant secondary.

astro-ph.HE↗
arXiv2015

The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension

We introduce a new interacting (stochastic) particle system q-PushASEP which interpolates between the q-TASEP introduced by Borodin and Corwin (see arXiv:1111.4408, and also arXiv:1207.5035; arXiv:1305.2972; arXiv:1212.6716) and the q-PushTASEP introduced recently by Borodin and Petrov (arXiv:1305.5501). In the q-PushASEP, particles can jump to the left or to the right, and there is a certain partially asymmetric pushing mechanism present. This particle system has a nice interpretation as a model of traffic on a one-lane highway in which cars are able to accelerate or slow down. Using the quantum many body system approach, we explicitly compute the expectations of a large family of observables for this system in terms of nested contour integrals. We also discuss relevant Fredholm determinantal formulas for the distribution of the location of each particle, and connections of the model with a certain two-sided version of Macdonald processes and with the semi-discrete stochastic heat equation.

math.PR↗
arXiv2015

Law of Large Numbers for Infinite Random Matrices over a Finite Field

Asymptotic representation theory of general linear groups GL(n,q) over a finite field leads to studying probability measures ρon the group U of all infinite uni-uppertriangular matrices over F_q, with the condition that ρis invariant under conjugations by arbitrary infinite matrices. Such probability measures form an infinite-dimensional simplex, and the description of its extreme points (in other words, ergodic measures ρ) was conjectured by Kerov in connection with nonnegative specializations of Hall-Littlewood symmetric functions. Vershik and Kerov also conjectured the following Law of Large Numbers. Consider an n by n diagonal submatrix of the infinite random matrix drawn from an ergodic measure coming from the Kerov's conjectural classification. The sizes of Jordan blocks of the submatrix can be interpreted as a (random) partition of n, or, equivalently, as a (random) Young diagram λ(n) with n boxes. Then, as n goes to infinity, the rows and columns of λ(n) have almost sure limiting frequencies corresponding to parameters of this ergodic measure. Our main result is the proof of this Law of Large Numbers. We achieve it by analyzing a new randomized Robinson-Schensted-Knuth (RSK) insertion algorithm which samples random Young diagrams λ(n) coming from ergodic measures. The probability weights of these Young diagrams are expressed in terms of Hall-Littlewood symmetric functions. Our insertion algorithm is a modified and extended version of a recent construction by Borodin and the second author (arXiv:1305.5501). On the other hand, our randomized RSK insertion generalizes a version of the RSK insertion introduced by Vershik and Kerov (1986) in connection with asymptotic representation theory of symmetric groups (which is governed by nonnegative specializations of Schur symmetric functions).

math.PR↗
arXiv2015

The International Mass Loading Service

The International Mass Loading Service computes four loadings: a) atmospheric pressure loading; b) land water storage loading; c) oceanic tidal loading; and d) non-tidal oceanic loading. The service provides to users the mass loading time series in three forms: 1) pre-computed time series for a list of 849 space geodesy stations; 2) pre-computed time series on the global 1deg x 1deg grid; and 3) on-demand Internet service for a list of stations and a time range specified by the user. The loading displacements are provided for the time period from 1979.01.01 through present, updated on an hourly basis, and have latencies 8-20 hours.

physics.geo-ph↗
arXiv2015

Modeling of path delay in the neutral atmosphere: a paradigm shift

Computation of propagation effects in the neutral atmosphere, namely path delay, extinction, and bending angle is a trivial task provided the 4D state of the atmosphere is known. Unfortunately, the mixing ratio of water vapor is highly variable and it cannot be deduced from surface measurements. That fact led to a paradigm that considers path delay and extinction in the atmosphere as a~priori unknown quantities that have to be evaluated from the radio astronomy data themselves. Development of our ability to model the atmosphere and to digest humongous outputs of these models that took place over the course of the 21st century changed the game. Using the publicly available output of operational numerical weather model GEOS run by NASA, we are in a position to compute path delay through the neutral atmosphere for any station and for any epoch from 1979 through now with accuracy of 45 ps * cosec elevation. We are in a position to compute extinction with accuracy better than 10 pro cents. We are in a position to do it routinely, in a similar way how we update apparent star positions for precession and nutation. Moreover, we are in a position to do it now. As a demonstration of current capabilities, I have computed time series of path delays for all radiotelecopes that I was aware of (220 sites) since 1979 with a step 3-6 hours. Results of the validation tests are presented. A new paradigm of data analysis assumes that we know the atmosphere propagation effects a priori with the accuracy higher that one could deduce them from radio astronomy observations.

astro-ph.IM↗
arXiv2015

New Associations of Gamma-Ray Sources from the Fermi Second Source Catalog

We present the results of an all-sky radio survey between 5 and 9 GHz of the fields surrounding all unassociated gamma-ray objects listed in the Fermi Large Area Telescope Second Source Catalog (2FGL). The goal of these observations is to find all new gamma-ray AGN associations with radio sources >10 mJy at 8 GHz. We observed with the Very Large Array and the Australia Telescope Compact Array the areas around unassociated sources, providing localizations of weak radio point sources found in 2FGL fields at arcmin scales. Then we followed-up a subset of those with the Very Long Baseline and the Long Baseline Arrays to confirm detections of radio emission on parsec-scales. We quantified association probabilities based on known statistics of source counts and assuming a uniform distribution of background sources. In total we found 865 radio sources at arcsec scales as candidates for association and detected 95 of 170 selected for follow-up observations at milliarcsecond resolution. Based on this we obtained firm associations for 76 previously unknown gamma-ray AGN. Comparison of these new AGN associations with the predictions from using the WISE color-color diagram shows that half of the associations are missed. We found that 129 out of 588 observed gamma-ray sources at arcmin scales not a single radio continuum source was detected above our sensitivity limit within the 3-sigma gamma-ray localization. These "empty" fields were found to be particularly concentrated at low Galactic latitudes. The nature of these Galactic gamma-ray emitters is not yet determined.

astro-ph.HE↗
arXiv2015

Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field

We study large-scale height fluctuations of random stepped surfaces corresponding to uniformly random lozenge tilings of polygons on the triangular lattice. For a class of polygons (which allows arbitrarily large number of sides), we show that these fluctuations are asymptotically governed by a Gaussian free (massless) field. This complements the similar result obtained in Kenyon [Comm. Math. Phys. 281 (2008) 675-709] about tilings of regions without frozen facets of the limit shape. In our asymptotic analysis we use the explicit double contour integral formula for the determinantal correlation kernel of the model obtained previously in Petrov [Asymptotics of random lozenge tilings via Gelfand-Tsetlin schemes (2012) Preprint].

math.PR↗