Continuous time `true' self-avoiding random walk on Z

TL;DR

This paper studies a continuous-time self-avoiding random walk on the integer line, establishing limit theorems for its local time and displacement using a modified Ray-Knight approach.

Contribution

It extends the Ray-Knight method to continuous-time self-avoiding walks, providing new limit theorems for local time and displacement.

Findings

Limit theorem for the local time of the walk

Local limit theorem for the displacement

Method adaptation for continuous-time models

Abstract

We consider the continuous time version of the `true' or `myopic' self-avoiding random walk with site repulsion in 1d. The Ray-Knight-type method which was applied to the discrete time and edge repulsion case, is applicable to this model with some modifications. We present a limit theorem for the local time of the walk and a local limit theorem for the displacement.