First passage time distribution for a random walker on a random forcing energy landscape

TL;DR

This paper introduces an analytical approximation method for the first passage time distribution of a random walker on a complex energy landscape, validated through numerical simulations, advancing understanding of stochastic processes in disordered systems.

Contribution

It provides a novel approximation scheme that accurately captures the entire distribution of first passage times on a random forcing energy landscape.

Findings

Approximation scheme matches numerical simulations across all timescales.

The method effectively characterizes first passage time distributions in disordered systems.

Results improve analytical understanding of stochastic processes on complex energy landscapes.

Abstract

We present an analytical approximation scheme for the first passage time distribution on a finite interval of a random walker on a random forcing energy landscape. The approximation scheme captures the behavior of the distribution over all timescales in the problem. The results are carefully checked against numerical simulations.