Markov processes of infinitely many nonintersecting random walks

• 成果类型: Article
• 署名作者: Borodin, Alexei; Gorin, Vadim
• 署名单位: Massachusetts Institute of Technology (MIT); California Institute of Technology; Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0417-4
• 发表日期: 2013
• 页码: 935-997
• 关键词: Asymptotics; paths

摘要

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.