English

Limit Theorems for Random Walks in the Hyperbolic Space

Probability 2023-12-12 v1

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.

Keywords

Cite

@article{arxiv.2312.06222,
  title  = {Limit Theorems for Random Walks in the Hyperbolic Space},
  author = {V Konakov and S Menozzi},
  journal= {arXiv preprint arXiv:2312.06222},
  year   = {2023}
}
R2 v1 2026-06-28T13:46:51.292Z