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Determinantal martingales and noncolliding diffusion processes

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  • Katori, Makoto

Abstract

Two aspects of noncolliding diffusion processes have been extensively studied. One of them is the fact that they are realized as harmonic Doob transforms of absorbing particle systems in the Weyl chambers. Another aspect is integrability in the sense that any spatio-temporal correlation function can be expressed by a determinant. The purpose of the present paper is to clarify the connection between these two aspects. We introduce a notion of determinantal martingale and prove that, if the system has determinantal-martingale representation, then it is determinantal. In order to demonstrate the direct connection between the two aspects, we study three processes.

Suggested Citation

  • Katori, Makoto, 2014. "Determinantal martingales and noncolliding diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3724-3768.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:11:p:3724-3768
    DOI: 10.1016/j.spa.2014.06.002
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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.
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    Cited by:

    1. 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.

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