Perturbed GUE Minor Process and Warren's Process with Drifts

TL;DR

This paper studies a matrix diffusion process with constant drifts, providing explicit correlation kernels, and connects it to Warren's process and a particle system in the KPZ class, extending previous zero-drift results.

Contribution

It introduces a determinantal process for Hermitian matrix diffusions with drifts and links it to Warren's process and KPZ class particle systems, generalizing existing zero-drift findings.

Findings

Explicit correlation kernel for the process

Connection to Warren's process with level-dependent drifts

Diffusion limit from an interacting particle system in KPZ class

Abstract

We consider the minor process of (Hermitian) matrix diffusions with constant diagonal drifts. At any given time, this process is determinantal and we provide an explicit expression for its correlation kernel. This is a measure on the Gelfand-Tsetlin pattern that also appears in a generalization of Warren's process, in which Brownian motions have level-dependent drifts. Finally, we show that this process arises in a diffusion scaling limit from an interacting particle system in the anisotropic KPZ class in 2+1 dimensions. Our results generalize the known results for the zero drift situation.