Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers
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.
scientific article; zbMATH DE number 54722
scientific article