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.
UR - https://www.scopus.com/pages/publications/33845755341
UR - https://www.scopus.com/pages/publications/33845755341#tab=citedBy
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 -