Limit Theorems for Random Walks in the Hyperbolic Space

Published 11 Dec 2023 in math.PR | (2312.06222v1)

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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