Strong Markov property of determinantal processes with extended kernels

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Osada, Hirofumi¹  Tanemura, Hideki² 

[1] Kyushu Univ, Fac Math, Fukuoka 8190395, Japan

[2] Chiba Univ, Fac Sci, Dept Math & Informat, Inage Ku, Chiba 2638522, Japan

关键词: Determinantal processes;    Correlation kernels;    Random matrix theory;    Infinite particle systems;    Strong Markov property;    Entire function and topology;   

DOI  :  10.1016/j.spa.2015.08.003

来源: Elsevier

【 摘 要 】

Noncolliding Brownian motion (Dyson's Brownian motion model with parameter beta = 2) and non-colliding 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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free