Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers
type: Item
instance of: scholarly article
title: Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers
zbMATH Open document ID: 0749.60022
DOI: 10.1007/BF02099260
author: S. Singh
published in: Communications in Mathematical Physics
publication date: 1992-09-26T00:00:00Z
review text: The following one-dimensional model is considered: a point particle of mass \(M\), confined to the unit interval \([0,1]\) is surrounded by an infinite ideal gas of point particles (atoms) of unit mass. The molecule interacts with the atoms and walls via elastic collisions. Two versions of the model are considered. In the first version the atoms are situated to the right of the molecule while in the second one they are situated on the whole line. For both cases it is proven that the central limit theorem holds for the following quantities: (i) the number of collisions of the molecule with both walls until the time \(T\), (ii) the molecular path until \(T\) (see, however, note added in proof). Some remarks are made concerning the multidimensional case.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 82B99
Mathematics Subject Classification ID: 82D05
Mathematics Subject Classification ID: 82C22
zbMATH DE Number: 54722
zbMATH Keywords: Rayleigh gas
zbMATH Keywords: central limit theorem
zbMATH Keywords: Brownian motion
reviewed by: Paweł Maślanka
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02099260
OpenAlex ID: W2066810862
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description: scientific article; zbMATH DE number 54722