Observables of Macdonald processes

TL;DR

This paper introduces a new framework for calculating averages of observables in Macdonald processes, providing contour-integral formulas and Fredholm determinants for various multilevel and single-level observables.

Contribution

It develops a novel computational framework that extends the understanding of Macdonald processes through explicit formulas and determinant representations.

Findings

Derived new contour-integral formulas for multilevel observables

Established Fredholm determinant formulas for single-level observables

Enhanced computational tools for analyzing Macdonald processes

Abstract

We present a framework for computing averages of various observables of Macdonald processes. This leads to new contour--integral formulas for averages of a large class of multilevel observables, as well as Fredholm determinants for averages of two different single level observables.