arXiv subjects

Leonid Petrov

Publications and source records attributed to Leonid Petrov.

98 records · Page 6Linked to original sources

arXiv2009

Random Walks on Strict Partitions

We consider a certain sequence of random walks. The state space of the n-th random walk is the set of all strict partitions of n (that is, partitions without equal parts). We prove that, as n goes to infinity, these random walks converge to a continuous-time Markov process. The state space of this process is the infinite-dimensional simplex consisting of all nonincreasing infinite sequences of nonnegative numbers with sum less than or equal to one. The main result about the limit process is the expression of its the pre-generator as a formal second order differential operator in a polynomial algebra. Of separate interest is the generalization of Kerov interlacing coordinates to the case of shifted Young diagrams.

math.PR↗

arXiv2009

The use of the Long Baseline Array in Australia for precise geodesy and absolute astrometry

We report the results of a successful 12 hour 22 GHz VLBI experiment using a heterogeneous network that includes radio telescopes of the Long Baseline Array (LBA) in Australia and several VLBI stations that regularly observe in geodetic VLBI campaigns. We have determined positions of three VLBI stations, ATCA-104, CEDUNA and MOPRA, with an accuracy of 4-30mm using a novel technique of data analysis. These stations have never before participated in geodetic experiments. We observed 105 radio sources, and amongst them 5 objects which have not previously been observed with VLBI. We have determined positions of these new sources with the accuracy of 2-5 mas. We make conclusion that the LBA network is capable of conducting absolute astrometry VLBI surveys with accuracy better than 5 mas.

physics.geo-ph↗

arXiv2009

Precise geodesy with the Very Long Baseline Array

We report on a program of geodetic measurements between 1994 and 2007 which used the Very Long Baseline Array and up to 10 globally distributed antennas. One of the goals of this program was to monitor positions of the array at a 1 millimeter level of accuracy and to tie the VLBA into the International Terrestrial Reference Frame. We describe the analysis of these data and report several interesting geophysical results including measured station displacements due to crustal motion, earthquakes, and antenna tilt. In terms of both formal errors and observed scatter, these sessions are among the very best geodetic VLBI experiments.

physics.geo-ph↗

arXiv2008

A Two-Parameter Family of Infinite-Dimensional Diffusions in the Kingman Simplex

The aim of the paper is to introduce a two-parameter family of infinite-dimensional diffusion processes X(alpha,theta) related to Pitman's two-parameter Poisson-Dirichlet distributions PD(alpha,theta). The diffusions X(alpha,theta) are obtained in a scaling limit transition from certain finite Markov chains on partitions of natural numbers. The state space of X(alpha,theta) is an infinite-dimensional simplex called the Kingman simplex. In the special case when parameter alpha vanishes, our finite Markov chains are similar to Moran-type model in population genetics, and our diffusion processes reduce to the infinitely-many-neutral-alleles diffusion model studied by Ethier and Kurtz (1981). Our main results extend those of Ethier and Kurtz to the two-parameter case and are as follows: The Poisson-Dirichlet distribution PD(alpha,theta) is a unique stationary distribution for the corresponding process X(alpha,theta); the process is ergodic and reversible; the spectrum of its generator is explicitly described. The general two-parameter case seems to fall outside the setting of models of population genetics, and our approach differs in some aspects from that of Ethier and Kurtz. We also consider the case of degenerate series of parameters alpha and theta and conclude that the diffusions in finite-dimensional simplexes studied by Ethier and Kurtz (1981) arise as a special case of our two-parameter family of diffusions.

math.PR↗

arXiv2007

On observability of the free core nutation

Neither astronomical technique, including VLBI, can measure nutation directly. Estimates of parameters of the nutation model are produced by solving the LSQ problem of adjusting millions parameters using estimates of group delay. The choice of the mathematical model for nutation used in the estimation process of analysis of group delays affects our ability to interpret the results. Ignoring these subtleties and using parameters of the nutation model either in the form of time series, or in the form of empirical expansion as "VLBI measurement of nutation", opens a room for misinterpretation and mistakes. Detailed analysis of the problem reveals that the separation of forced nutations, atmospheric nutations, ocean nutations, and the retrograde free core nutation requires invoking some hypotheses, and beyond a specific level becomes uncertain. This sets a limit of our ability to make an inference about the free core nutation.

physics.geo-ph↗

arXiv2003

Study of the atmospheric pressure loading signal in VLBI observations

Redistribution of air masses due to atmospheric circulation causes loading deformation of the Earth's crust which can be as large as 20 mm for the vertical component and 3 mm for horizontal components. Rigorous computation of site displacements caused by pressure loading requires knowledge of the surface pressure field over the entire Earth surface. A procedure for computing 3-D displacements of geodetic sites of interest using a 6-hourly pressure field from the NCEP numerical weather models and the Ponte and Ray [2002] model of atmospheric tides is presented. We investigated possible error sources and found that the errors of our pressure loading time series are below the 15% level. We validated our model by estimating the admittance factors of the pressure loading time series using a dataset of 3.5 million VLBI observations from 1980 to 2002. The admittance factors averaged over all sites are 0.95 -+ 0.02 for the vertical displacement and 1.00 -+ 0.07 for the horizontal displacements. For the first time horizontal displacements caused by atmospheric pressure loading have been detected. The closeness of these admittance factors to unity allows us to conclude that on average our model quantitatively agrees with the observations within the error budget of the model. At the same time we found that the model is not accurate for several stations which are near a coast or in mountain regions. We conclude that our model is suitable for routine data reduction of space geodesy observations.

physics.geo-ph↗

arXiv2003

VLBA Calibrator Survey: Astrometric and Image Results

Positions and maps of 1608 new compact sources were obtained in twelve sessions observed during 1994--2002 at the VLBA network at 8.4/2.3 GHz. These sources are recommended for use as calibrators for phase reference imaging and as geodetic sources for astrometric/geodetic VLBI applications.

astro-ph↗

arXiv2003

Contribution of the VLBA Network to Geodynamics

A decade of observations in geodetic mode with the VLBA network gave valuable results. Approximately 1/5 of all geodetic observations are recorded in VLBA mode and processed at the Socorro correlator. Ten years of observations allowed us to reliably measure slow intra-plate motion of the VLBA stations located on the North-American plate. It also helped us to achieve scientific objectives of geodetic programs: verify models of harmonic and anharmonic site position variations caused by various loadings, improve models of core-mantle boundary, investigate mantle rheology and solve other tasks.

astro-ph↗