Journal
PROBABILITY THEORY AND RELATED FIELDS
Volume 155, Issue 3-4, Pages 935-997Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00440-012-0417-4
Keywords
Non-intersecting paths; Infinite-dimensional Markov process; Determinantal point process; Gelfand-Tsetlin scheme
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Funding
- NSF [DMS-1056390]
- Dynasty foundation
- RFBR-CNRS [10-01-93114]
- program Development of the scientific potential of the higher school
- Simons Foundation-IUM scholarship
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1056390] Funding Source: National Science Foundation
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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 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.
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