Stochastic dynamics of determinantal processes by integration by parts

TL;DR

This paper develops an integration by parts formula for determinantal processes, enabling the construction of a non-colliding diffusion process that has the determinantal process as its reversible distribution.

Contribution

It introduces a new integration by parts formula for determinantal processes and constructs a corresponding non-colliding diffusion process.

Findings

Existence of a non-colliding diffusion process with determinantal process distribution

Concrete example of the associated diffusion process

Extension of previous theoretical results

Abstract

We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and admits the distribution of the determinantal process as reversible law. In particular, this approach allows us to build a concrete example of the associated diffusion process, providing an illustration of the results of [4] and [30].