Markov processes of infinitely many nonintersecting random walks

作者：Borodin Alexei; Gorin Vadim^*

来源：Probability Theory and Related Fields, 2013, 155(3-4): 935-997.

DOI：10.1007/s00440-012-0417-4

• Non-intersecting paths
• Infinite-dimensional Markov process
• Determinantal point process
• Gelfand-Tsetlin scheme

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.

• 出版日期2013-4