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Central limit theorem for periodic Lorentz gas free path length

Paper Authors:

Songzi Li

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Proves central limit theorem for periodic Lorentz gas free path length

Connects free path distribution to dynamics on lattice space

Obtains asymptotic formula for distribution function

Derives central limit theorem for lattice point counting function

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Central limit theorem for periodic Lorentz gas free path length

This paper proves the central limit theorem for the free path length in the Boltzmann-Grad limit of the periodic Lorentz gas. The proof relies on connecting the free path length distribution to dynamics of expanding translates of a unipotent subgroup on the lattice space SL(d,R)/SL(d,Z), as described in prior work by Marklof and Strömbergsson. An asymptotic formula for the free path length distribution function is also obtained. Additionally, a central limit theorem is derived for the counting function in a related lattice point problem.

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