The problem of recurrence for Lorentz processes
type: Item
instance of: scholarly article
title: The problem of recurrence for Lorentz processes
zbMATH Open document ID: 0573.60095
DOI: 10.1007/BF01209329
author: András Krámli
author: D. Szász
published in: Communications in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: We prove that, for the planar Lorentz process with a periodic configuration of scatterers, the quasi-local CLT of the Gaussian \(\{\log^{\rho}n\}\) type holds for any \(\rho >1\). Consequently, for arbitrary \(\rho >3/2\), the probabilities that, at the moment of the nth reflection, this process lies in a square of size \(\log^{\rho}n\) are asymptotically Gaussian. This implies that these events occur for infinitely many values of n (i.e. a weaker form of recurrence).
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 81P20
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 3915382
zbMATH Keywords: statistical properties of the Lorentz process
zbMATH Keywords: Cramér-Edgeworth- Tchebysheff type expansions
zbMATH Keywords: planar Lorentz process
zbMATH Keywords: periodic configuration of scatterers
zbMATH Keywords: reflection
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01209329
OpenAlex ID: W2051388946
description: scientific article; zbMATH DE number 3915382