Eynard-Mehta theorem, Schur process, and their pfaffian analogs

TL;DR

This paper provides straightforward linear algebra proofs of key theorems related to the Schur process and its Pfaffian analogs, enhancing understanding of determinantal and Pfaffian processes.

Contribution

It introduces simple linear algebraic proofs for the Eynard-Mehta theorem, Okounkov-Reshetikhin formula, and Pfaffian analogs, and discusses properties of determinantal and Pfaffian process spaces.

Findings

Linear algebraic proofs of key theorems

Clarification of properties of determinantal and Pfaffian processes

Extension of formulas to Pfaffian analogs

Abstract

We give simple linear algebraic proofs of Eynard-Mehta theorem, Okounkov-Reshetikhin formula for the correlation kernel of the Schur process, and Pfaffian analogs of these results. We also discuss certain general properties of the spaces of all determinantal and Pfaffian processes on a given finite set.