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arXiv · 2507.15902

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

Chevalier Guillaume
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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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Chevalier Guillaume. 2025-07-21. The dependency digraph for irreducible finite-range random walk in free groups. https://arxiv.org/abs/2507.15902

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