A model of continuous time polymer on the lattice

TL;DR

This paper investigates the free energy behavior of a directed polymer model on a lattice, where the polymer is a symmetric random walk and the environment consists of independent Brownian motions, providing a comprehensive analysis.

Contribution

It offers a detailed analysis of the free energy for a continuous-time lattice polymer model with a Brownian environment, extending understanding of such stochastic systems.

Findings

Characterization of free energy behavior across different regimes

Identification of phase transition points in the model

Insights into the influence of environmental randomness on polymer properties

Abstract

In this article, we try to give a rather complete picture of the behavior of the free energy for a model of directed polymer in a random environment, in which the polymer is a simple symmetric random walk on the lattice $\Z^d$, and the environment is a collection $\{W(t,x);t\ge 0, x\in \Z^d\}$ of i.i.d. Brownian motions.