Sample Path Large Deviations for Random Walks on Regular Trees

Jie Jiang; Shuwen Lai

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arXiv · 2505.03324

Sample Path Large Deviations for Random Walks on Regular Trees

Jie Jiang·Shuwen Lai

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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.

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Jie Jiang, Shuwen Lai. 2025-05-06. Sample Path Large Deviations for Random Walks on Regular Trees. https://arxiv.org/abs/2505.03324

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