Strong Markov property of determinantal processes with extended kernels

Hirofumi Osada, Hideki Tanemura

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Noncolliding Brownian motion (Dyson's Brownian motion model with parameter β=2) and noncolliding Bessel processes are determinantal processes; that is, their space-time correlation functions are represented by determinants. Under a proper scaling limit, such as the bulk, soft-edge and hard-edge scaling limits, these processes converge to determinantal processes describing systems with an infinite number of particles. The main purpose of this paper is to show the strong Markov property of these limit processes, which are determinantal processes with the extended sine kernel, extended Airy kernel and extended Bessel kernel, respectively. We also determine the quasi-regular Dirichlet forms and infinite-dimensional stochastic differential equations associated with the determinantal processes.

Original languageEnglish
Pages (from-to)186-208
Number of pages23
JournalStochastic Processes and their Applications
Volume126
Issue number1
DOIs
Publication statusPublished - 2016 Jan 1
Externally publishedYes

Keywords

  • 30C15
  • 47D07
  • 60G55
  • 82C22
  • MSC 15B52

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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