On large deviation rate functions for a continuous-time directed polymer in weak disorder

TL;DR

This paper demonstrates that in the weak disorder phase, the large deviation rate function for the endpoint of a continuous-time directed polymer matches that of the underlying random walk near the origin, revealing a phase-specific behavior.

Contribution

It establishes the equivalence of the large deviation rate functions for the polymer endpoint and the underlying random walk in the weak disorder phase.

Findings

Rate function for the polymer endpoint matches the underlying walk near the origin in weak disorder.

The result holds throughout the entire weak disorder phase.

Provides insight into the phase-specific behavior of directed polymers.

Abstract

We show that the endpoint large deviation rate function for a continuous-time directed polymer agrees with the rate function of the underlying random walk near the origin in the whole weak disorder phase.