First-passage percolation on ladder-like graphs with heterogeneous exponential times

TL;DR

This paper analyzes the asymptotic speed of first-passage percolation on ladder-like graphs with heterogeneous exponential edge times, using Markov chain methods to handle varying means.

Contribution

It introduces a novel approach employing Markov chain analysis to determine asymptotic speeds in heterogeneous exponential first-passage percolation on ladder graphs.

Findings

Asymptotic speed formulas derived for heterogeneous exponential edge times

Method applicable to width-2 ladder-like graphs with independent edge times

Stationary distribution properties of the associated Markov chain are key to the analysis

Abstract

We determine the asymptotic speed of the first-passage percolation process on some ladder-like graphs (or width-2 stretches) when the times associated with different edges are independent and exponentially distributed but not necessarily all with the same mean. The method uses a particular Markov chain associated with the first-passage percolation process and properties of its stationary distribution.