A local limit theorem on certain \(p\)-adic groups and buildings
type: Item
instance of: scholarly article
title: A local limit theorem on certain \(p\)-adic groups and buildings
zbMATH Open document ID: 1005.60018
author: Filippo Tolli
published in: Monatshefte für Mathematik
publication date: 2002-06-27T00:00:00Z
review text: The author investigates local central limit theorems for finite range random walks on certain \(p\)-adic groups and buildings. In particular, for biinvariant, aperiodic irreducible random walks with finite range, an explicit formula is derived together with Berry-Esseen-type estimates for the error. This result is closely related to the local limit theorems on the \(\widetilde A_d\)-buildings in recent papers of \textit{D. Cartwright} and \textit{W. Woess} (Preprint) and \textit{M. Lindlbauer} and the reviewer [J. Aust. Math. Soc. 73, 301-334 (2002)]. Moreover, the author proves a local limit theorem for arbitrary aperiodic, symmetric, and irreducible random walks with finite range on certain \(p\)-adic groups. This interesting result supplements well-known results of S. Lalley and others for not necessarily isotropic random walks on free groups and homogeneous trees.
reviewed by: Michael Voit
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 22E35
Mathematics Subject Classification ID: 43A30
zbMATH DE Number: 1761118
zbMATH Keywords: random walks with finite range
zbMATH Keywords: \(p\)-adic groups
zbMATH Keywords: buildings
zbMATH Keywords: local limit theorems
MaRDI profile type: Publication
full work available at URL: s006050170030
OpenAlex ID: W2094654171
DOI: 10.1007/S006050170030
description: scientific article; zbMATH DE number 1761118