Sharp estimates for distinguished random walks on affine buildings of type Ar

2023/12/04 by Jean-Philippe Anker, Bruno Schapira, Anker, Jean-Philippe +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2312.01781

openalex publication_date 2023/12/04 · openalex created_date 2023/12/05 · openalex updated_date 2026/07/28

Abstract

We study a distinguished random walk on affine buildings of type Ar , which was already considered by Cartwright, Saloff-Coste and Woess. In rank r=2, it is the simple random walk and we obtain optimal global bounds for its transition density (same upper and lower bound, up to multiplicative constants). In the higher rank case, we obtain sharp uniform bounds in fairly large space-time regions which are sufficient for most applications.

Citations

• Martin compactifications of affine buildings

Cited by

• Mass Functions and Asymptotic Behavior of Caloric Functions on Affine Buildings

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