Spectral Radius of Biased Random Walks on Regular Trees

TL;DR

This paper analyzes the spectral properties of biased random walks on regular trees, providing explicit calculations of the spectral radius, first return probability, and n-step transition probabilities.

Contribution

It introduces new analytical results for spectral radius and transition probabilities of biased random walks on regular trees.

Findings

Spectral radius of biased random walks is explicitly derived.

First return probabilities are calculated for the biased case.

n-step transition probabilities are obtained for regular trees.

Abstract

We consider biased random walk on regular tree and we obtain the spectral radius, first return probability and $n$-step transition probability.