Limit Theorems for Random Walks in the Hyperbolic Space

V. D. Konakov; S. Menozzi

doi:10.1134/S0001434625030083

Limit Theorems for Random Walks in the Hyperbolic Space

V. D. Konakov
, S. Menozzi

National Research University
Université d'Evry Val d'Essonne

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Abstract: A local limit theorem for random walks in the hyperbolic Poincaré space of dimension 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.

Original language	English
Pages (from-to)	425-441
Number of pages	17
Journal	Mathematical Notes
Volume	117
Issue number	3
DOIs	https://doi.org/10.1134/S0001434625030083
Publication status	Published - 1 Apr 2025
Externally published	Yes

Keywords

hyperbolic space
local limit theorems
random walks and Brownian motion

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10.1134/S0001434625030083

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title = "Limit Theorems for Random Walks in the Hyperbolic Space",

abstract = "Abstract: A local limit theorem for random walks in the hyperbolic Poincar{\'e} space of dimension is proved. To this end, we use the model of a ball and describe the walk in it by means of the M{\"o}bius addition and multiplication. This also enables us to derive the corresponding law of large numbers.",

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Y1 - 2025/4/1

N2 - Abstract: A local limit theorem for random walks in the hyperbolic Poincaré space of dimension 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.

AB - Abstract: A local limit theorem for random walks in the hyperbolic Poincaré space of dimension 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.

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KW - local limit theorems

KW - random walks and Brownian motion

UR - https://www.scopus.com/pages/publications/105008237365

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DO - 10.1134/S0001434625030083

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JF - Mathematical Notes

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ER -

Limit Theorems for Random Walks in the Hyperbolic Space

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Keywords

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