On the distribution of free path lengths for the periodic Lorentz gas. III.

DOI10.1007/S00220-003-0825-5zbMATH Open1041.82016arXivmath/0301300OpenAlexW2996565864MaRDI QIDQ1416854

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Publication date: 16 December 2003

Published in: (Search for Journal in Brave)

Abstract: In a flat 2-torus with a disk of diameter $r$ removed, let $Ph{i}_r(t)$ be the distribution of free-path lengths (the probability that a segment of length larger than $t$ with uniformly distributed origin and direction does not meet the disk). We prove that $Ph{i}_r(t/r)$ behaves like $frac2p{i}^{2}t$ for each $t>2$ and in the limit as $ro{0}^{+}$, in some appropriate sense. We then discuss the implications of this result in the context of kinetic theory.

Full work available at URL: https://arxiv.org/abs/math/0301300

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