Limit Theorems for Random Walks in the Hyperbolic Space

V Konakov; S Menozzi

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arXiv · 2312.06222

Limit Theorems for Random Walks in the Hyperbolic Space

V Konakov·S Menozzi

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Abstract

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

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V Konakov, S Menozzi. 2023-12-11. Limit Theorems for Random Walks in the Hyperbolic Space. https://arxiv.org/abs/2312.06222

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