Determinantal martingales and noncolliding diffusion processes

作者：Katori Makoto^*

来源：Stochastic Processes and Their Applications, 2014, 124(11): 3724-3768.

DOI：10.1016/j.spa.2014.06.002

• Noncolliding diffusion processes
• Harmonic Doob transforms
• Martingales
• Determinantal processes
• Random matrix theory

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.

• 出版日期2014-11