A law of large numbers for the range of rotor walks on periodic trees

TL;DR

This paper establishes a law of large numbers for the growth of the range of recurrent rotor walks with random initial states on a broad class of trees called periodic trees.

Contribution

It proves a law of large numbers for the range of rotor walks on periodic trees, extending understanding of their long-term behavior.

Findings

Range size grows proportionally with time in recurrent rotor walks.

The result applies to a general class of trees called periodic trees.

Provides a theoretical foundation for analyzing rotor walk dynamics.

Abstract

The aim of the current work is to prove a law of large numbers for the range size of recurrent rotor walks with random initial configuration on a general class of trees, called periodic trees or directed covers of graphs.