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.
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}
}