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

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.

arXiv comment8 pages, minor revision made for publication

References in corpus (4)

• Scaling for a one-dimensional directed polymer with boundary conditions
• Differing averaged and quenched large deviations for random walks in random environments in dimensions two and three
• Large deviations for random walk in a space--time product environment
• Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher