Sample Path Large Deviations for Random Walks on Regular Trees

2025/05/06 by Jie Jiang, Jiang, Jie, Shuwen Lai +1
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2505.03324

openalex publication_date 2025/05/06 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

This paper investigates the large deviation problem in the sample path space of the nearest-neighbor random walks on regular trees. We establish the sample path large deviation principle for the law of the distance from a nearest random walk on a regular tree to the root with a good convex rate function. Furthermore, we derive an implicit expression for the rate function via the Fenchel-Legendre transform of the log-moment generating function.

Citations

• Multifractal spectrum of branching random walks on free groups
• Large deviations for random walks on free products of finitely generated groups
• Long Brownian bridges in hyperbolic spaces converge to Brownian trees

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