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This is a Quantitative Study study.

September 22, 2025Open Access

The dependency digraph for irreducible finite-range random walk in free groups

Key Points

The study provides insights into the behavior of irreducible finite-range random walks, emphasizing their dependency digraph structure.
Analytic and geometric properties of objects related to these walks are explored, focusing on how they interact in free groups.
New definitions, such as the flooded cavern tree, support detailed analyses of the dependency digraphs introduced.
The findings contribute to a broader understanding of asymptotic expansions linked to random walks and their probabilities.

Abstract

This article is one of a triptych composed with Che25a and Che25b, that aims at proving an asymptotic expansion to any order of the passage probability of an irreducible equivariant finite range random walk on a tree. In this text we study the analytic and geometric properties of the objects introduced in Che25b. To do so we introduce the definition of a ''flooded cavern tree'' enabling a precise study of some dependency digraph associated with a given irreducible finite-range random walk on a free group.

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Cite This Study

C. Benoît à la Guillaume (Mon,) studied this question.

synapsesocial.com/papers/68d46fdc31b076d99fa6a6ab https://doi.org/https://doi.org/10.48550/arxiv.2507.15902

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