User lazycat - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T09:26:49Z http://mathoverflow.net/feeds/user/21005 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/110327/what-time-does-it-take-for-irrational-rotations-to-hit-an-interval/110958#110958 Answer by LazyCat for What time does it take for irrational rotations to hit an interval? LazyCat 2012-10-29T03:04:33Z 2012-10-29T03:04:33Z <p>There is a theorem of Kesten, which roughly says, that if you take (\theta, \theta_0) random, and the number of times you hit (0, \alpha) in the first N iterations, subtract the expected N * \alpha, and normalize by \rho * ln(n), the result will converge to Cauchy distribution. This can be viewed as an analogue of CLT in this case. </p> http://mathoverflow.net/questions/105616/path-length-of-ball-on-tilted-perforated-plane/105677#105677 Answer by LazyCat for Path length of ball on tilted, perforated plane LazyCat 2012-08-28T02:55:08Z 2012-08-28T02:55:08Z <p>J. Marklof and A. Strömbergsson have pretty much complete results for the distribution you're interested in - both on the plane and in higher dimensions. Check </p> <p>J. Marklof and A. Strömbergsson, The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems, Annals of Mathematics 172 (2010) 1949–2033 </p> <p>J. Marklof and A. Strömbergsson, The Boltzmann-Grad limit of the periodic Lorentz gas, Annals of Mathematics 174 (2011) 225-298</p> http://mathoverflow.net/questions/86815/continuous-family-of-markov-chains/87089#87089 Answer by LazyCat for Continuous family of Markov chains LazyCat 2012-01-30T23:45:12Z 2012-01-30T23:45:12Z <p>Did you look at Doeblin condition? Don't have a proof, but I think it may help you. </p>