On strict monotonicity of the speed for excited random walks in one dimension

TL;DR

This paper provides a direct coupling proof demonstrating that the speed of one-dimensional multi-excited random walks with positive speed increases monotonically, extending previous results without relying on branching processes.

Contribution

It introduces a new coupling approach to prove strict monotonicity of the speed in excited random walks, avoiding the use of branching processes.

Findings

Proves strict monotonicity of the speed for 1D multi-excited random walks.

Extends previous results by Peterson.

Provides a coupling-based proof method.

Abstract

We give a "direct" coupling proof of strict monotonicity of the speed for 1-dimensional multi-excited random walks with positive speed. This reproves (and extends) a recent result of Peterson without using branching processes.