Markov processes of infinitely many nonintersecting random walks
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Borodin_Markov processes.pdf
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894.27 KB
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dc38172542445498f0fcedac41e4e3b4
Author(s)
Borodin, Alexei
Gorin, Vadim
Date Issued
March 2012
Journal
Probability Theory and Related Fields
Publisher
Springer-Verlag
Citation
Borodin, Alexei, and Vadim Gorin. “Markov processes of infinitely many nonintersecting random walks.” Probability Theory and Related Fields 155, no. 3 4 (April 14, 2013): 935-997.
Version
Original manuscript
Abstract
Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller Markov process. The dynamical correlation functions of the limit process are determinantal with an explicit correlation kernel. The key idea is to identify random point processes on Z with q-Gibbs measures on Gelfand–Tsetlin schemes and construct Markov processes on the latter space. Independently, we analyze the large time behavior of PushASEP with finitely many particles and particle-dependent jump rates (it arises as a marginal of our dynamics on Gelfand–Tsetlin schemes). The asymptotics is given by a product of a marginal of the GUE-minor process and geometric distributions.
Description
Original manuscript August 14, 2012
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/s00440-012-0417-4
