On the localization regime of high-dimensional directed polymers in time-correlated random field

TL;DR

This paper investigates the behavior of high-dimensional directed polymers in time-correlated random fields, establishing fundamental properties like free energy limits and identifying the transition between localized and delocalized phases.

Contribution

It provides new theoretical results on the existence, smoothness, and phase transition of directed polymers in complex correlated environments.

Findings

Proved law of large numbers for directed polymers in correlated fields

Established existence and smoothness of limiting free energies at all temperatures

Identified the delocalized-localized transition via entanglement separation techniques

Abstract

This paper describes directed polymer on general time-correlated random field. Law of large numbers, existence and smoothness of limiting free energies are proved at all temperature. We also display the delocalized-localized transition, via separating techniques for entanglement of the random field.