The two-time distribution in geometric last-passage percolation

TL;DR

This paper investigates the two-time distribution in geometric last-passage percolation, deriving its scaling limit expressed as a contour integral of a Fredholm determinant, advancing understanding of temporal correlations in the model.

Contribution

It provides the first explicit computation of the two-time distribution's scaling limit in geometric last-passage percolation, expressed via a Fredholm determinant.

Findings

Derived the scaling limit of the two-time distribution

Expressed the limit as a contour integral of a Fredholm determinant

Enhanced understanding of temporal correlations in geometric last-passage percolation

Abstract

We study the two-time distribution in directed last passage percolation with geometric weights in the first quadrant. We compute the scaling limit and show that it is given by a contour integral of a Fredholm determinant.