Strong Markov property of determinantal processes with extended kernels

Hirofumi Osada, Hideki Tanemura

    Research output: Contribution to journalArticlepeer-review

    9 Citations (Scopus)


    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
    Issue number1
    Publication statusPublished - Jan 1 2016

    All Science Journal Classification (ASJC) codes

    • Statistics and Probability
    • Modelling and Simulation
    • Applied Mathematics


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