This analysis demonstrates asymptotic expansions for passage probabilities in trees, highlighting geometric and analytic features of dependency digraphs.
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.
No takes yet. Share an insight, caveat, or question.
C. Benoît à la Guillaume (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: