TY - JOUR

T1 - The distribution of the free path lengths in the periodic two-dimensional Lorentz gas in the small-scatterer limit

AU - Boca, Florin P.

AU - Zaharescu, Alexandru

PY - 2007/1

Y1 - 2007/1

N2 - We study the free path length and the geometric free path length in the model of the periodic two-dimensional Lorentz gas (Sinai billiard). We give a complete and rigorous proof for the existence of their distributions in the small-scatterer limit and explicitly compute them. As a corollary one gets a complete proof for the existence of the constant term c = 2-3 ln 2+27ζ(3)/2Π2 in the asymptotic formula h(T) = -2 ln ε +c+o(1) of the KS entropy of the billiard map in this model, as conjectured by P. Dahlqvist.

AB - We study the free path length and the geometric free path length in the model of the periodic two-dimensional Lorentz gas (Sinai billiard). We give a complete and rigorous proof for the existence of their distributions in the small-scatterer limit and explicitly compute them. As a corollary one gets a complete proof for the existence of the constant term c = 2-3 ln 2+27ζ(3)/2Π2 in the asymptotic formula h(T) = -2 ln ε +c+o(1) of the KS entropy of the billiard map in this model, as conjectured by P. Dahlqvist.

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U2 - 10.1007/s00220-006-0137-7

DO - 10.1007/s00220-006-0137-7

M3 - Article

AN - SCOPUS:33845755341

SN - 0010-3616

VL - 269

SP - 425

EP - 471

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -