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Strong Markov property of determinantal processes with extended kernels

Author

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  • Osada, Hirofumi
  • Tanemura, Hideki

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.

Suggested Citation

  • Osada, Hirofumi & Tanemura, Hideki, 2016. "Strong Markov property of determinantal processes with extended kernels," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 186-208.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:1:p:186-208
    DOI: 10.1016/j.spa.2015.08.003
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    References listed on IDEAS

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    1. Osada, Hirofumi, 2013. "Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials II: Airy random point field," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 813-838.
    2. Katori, Makoto, 2014. "Determinantal martingales and noncolliding diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3724-3768.
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    Cited by:

    1. Yosuke Kawamoto & Hirofumi Osada, 2022. "Dynamical universality for random matrices," Partial Differential Equations and Applications, Springer, vol. 3(2), pages 1-51, April.
    2. Yosuke Kawamoto & Hirofumi Osada, 2019. "Dynamical Bulk Scaling Limit of Gaussian Unitary Ensembles and Stochastic Differential Equation Gaps," Journal of Theoretical Probability, Springer, vol. 32(2), pages 907-933, June.

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    1. Yosuke Kawamoto & Hirofumi Osada, 2019. "Dynamical Bulk Scaling Limit of Gaussian Unitary Ensembles and Stochastic Differential Equation Gaps," Journal of Theoretical Probability, Springer, vol. 32(2), pages 907-933, June.
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    4. Katori, Makoto, 2014. "Determinantal martingales and noncolliding diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3724-3768.

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