Annealed upper tails for the energy of a polymer

TL;DR

This paper investigates the probability of unusually high energy levels in a randomly charged symmetric transient random walk in three or more dimensions, deriving a large deviation principle and explicit rate functions.

Contribution

It provides the first large deviation principle and explicit rate functions for the upper tails of energy in such random walks with pairwise site interactions.

Findings

Established a large deviation principle for the energy distribution.

Derived explicit rate functions for a broad class of charge distributions.

Focused on annealed estimates in dimensions three and higher.

Abstract

We study the upper tails for the energy of a randomly charged symmetric and transient random walk. We assume that only charges on the same site interact pairwise. We consider annealed estimates, that is when we average over both randomness, in dimension three or more. We obtain a large deviation principle, and an explicit rate function for a large class of charge distributions.