Directed Random Walks on Colored, Periodic Lattices: A Gauge Theoretic Approach

TL;DR

This paper introduces a gauge-theoretic approach to analyze directed, colored, periodic lattices through random walks, providing analytic results and connecting to string theory gauge constructs.

Contribution

It presents a novel method linking gauge theory operator counting to random walks on specialized lattices, expanding analytical tools in this area.

Findings

Analytic solutions for random walks on directed, colored lattices.

Mapping of gauge operator counting to random walk problems.

Illustrative examples demonstrating the approach.

Abstract

We define a random walk problem which admits analytic results, on a class of infinite periodic lattices which are directed and colored. Our approach is motivated from the fact that such lattices arise in string theoretic constructs of certain gauge theories. An operator counting problem in the latter is mapped to a problem in random walks. This is illustrated with several examples.