Abstract:
For r(0,1), let Z r ={xR 2|dist(x,Z 2)>r/2} and define τ r (x,v)=inf{t>0|x+tv∂Z r }. Let Φ r (t) be the probability that τ r (x,v)≥t for x and v uniformly distributed in Z r and §1 respectively. We prove in this paper that
as t→+∞. This result improves upon the bounds on Φ r in Bourgain-Golse-Wennberg [Commun. Math. Phys. 190, 491–508 (1998)]. We also discuss the applications of this result in the context of kinetic theory.
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Received: 2 August 2002 / Accepted: 27 November 2002 Published online: 14 April 2003
Communicated by G. Gallavotti
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Caglioti, E., Golse, F. On the Distribution of Free Path Lengths for the Periodic Lorentz Gas III. Commun. Math. Phys. 236, 199–221 (2003). https://doi.org/10.1007/s00220-003-0825-5
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DOI: https://doi.org/10.1007/s00220-003-0825-5