Limit Theorems for Random Walks in the Hyperbolic Space

2023/12/11 by Valentin Konakov, Konakov, V, Stéphane Menozzi +1 · 1 citation
Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2312.06222

openalex publication_date 2023/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove central and local limit theorems for random walks on the Poincaré hyperbolic space of dimension n \v e 2. To this end we use the ball model and describe the walk therein through the Möbius addition and multiplication. This also allows to derive a corresponding law of large numbers.

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• Random walks on rank one symmetric spaces of noncompact type

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