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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2025 Volume 117, Issue 3, Pages 402–421 (Mi mzm14367)

Limit theorems for random walks in the hyperbolic space

V. D. Konakova, S. Menozzib

a National Research University Higher School of Economics, Moscow
b Université D'evry-val-D'essonne, Evry

Abstract: A local limit theorem for random walks in the hyperbolic Poincaré space of dimension $n\ge 2$ is proved. To this end, we use the model of a ball and describe the walk in it by means of the Möbius addition and multiplication. This also enables us to derive the corresponding law of large numbers.

Keywords: hyperbolic space, random walks and Brownian motion, local limit theorems.

UDC: 517

MSC: 60F99, 60J65

Received: 13.05.2024
Revised: 04.10.2024

DOI: 10.4213/mzm14367


 English version:
Mathematical Notes, 2025, 117:3, 425–441


© Steklov Math. Inst. of RAS, 2025