Correlation Functions of the Schur Process Through Macdonald Difference Operators

TL;DR

This paper presents a novel approach to deriving correlation functions of the Schur process by leveraging Macdonald difference operators, offering an alternative to traditional determinantal methods.

Contribution

It introduces a new method to compute Schur process correlation functions using Macdonald difference operators, expanding the theoretical toolkit.

Findings

Correlation functions expressed via Macdonald difference operators

Alternative derivation of determinantal structure

Enhanced understanding of Schur process properties

Abstract

Introduced by Okounkov and Reshetikhin, the Schur process is known to be a determinantal point process, meaning that its correlation functions are minors of a single correlation kernel matrix. Previously, this was derived using determinantal expressions for the skew-Schur polynomials. In this paper we obtain this result in a different way, using the fact that the Schur polynomials are eigenfunctions of Macdonald difference operators.