A short proof of diffusivity for the directed polymers in the weak disorder phase

TL;DR

This paper presents a concise and elementary proof demonstrating the diffusivity of directed polymers in a random environment within the weak disorder phase, simplifying previous approaches.

Contribution

It introduces a new, shorter proof technique for diffusivity in directed polymers under weak disorder, enhancing understanding and accessibility.

Findings

Proof of diffusivity in the weak disorder phase

Simplified and elementary proof method

Improved theoretical understanding of directed polymers

Abstract

We provide a new short and elementary proof of diffusivity for directed polymer in a random environment in the weak disorder phase.