Tail bounds for the O'Connell-Yor polymer

TL;DR

This paper establishes precise upper and lower tail bounds for the O'Connell-Yor polymer, advancing understanding of its deviation behavior using probabilistic and geometric methods.

Contribution

It provides the first tight bounds for tail probabilities of the O'Connell-Yor polymer in the moderate deviations regime, combining generating function identities with geometric techniques.

Findings

Derived bounds are of the correct order of magnitude.

Obtained strong tail estimates for transversal fluctuations.

Connected tail bounds to geometric and probabilistic techniques.

Abstract

We derive upper and lower bounds for the upper and lower tails of the O'Connell-Yor polymer of the correct order of magnitude via probabilistic and geometric techniques in the moderate deviations regime. The inputs of our work are an identity for the generating function of a two-parameter model of Rains and Emrah-Janjigian-Sepp\"al\"ainen, and the geometric techniques of Ganguly-Hegde and Basu-Ganguly-Hammond-Hegde. As an intermediate result we obtain strong tail estimates for the transversal fluctuation of the polymer path from the diagonal.