Francis Comets' Gumbel last passage percolation

TL;DR

This paper discusses a novel connection between a Gumbel last passage percolation model and the log-gamma directed polymer, including asymptotic analysis, inspired by Francis Comets' insights.

Contribution

It introduces a new relation between Gumbel last passage percolation and the log-gamma polymer, expanding understanding of directed polymer models.

Findings

Established a link between Gumbel percolation and log-gamma polymer

Derived asymptotic properties of the models

Honors Francis Comets' contributions to the field

Abstract

In 2015, Francis Comets shared with me a clever way to relate a model of directed last passage percolation with i.i.d. Gumbel edge weights to a special case of the log-gamma directed polymer model. To my knowledge, he never wrote this down. In the wake of his recent passing I am recording Francis' observation along with some associated asymptotics and discussion. This note is dedicated in memory of Francis whose work in the study of directed polymers defined and refined the field immensely.