5 papers
Limiting Distribution of Frobenius Numbers for
V. Shur, Ya. Sinai, A. Ustinov
The purpose of this paper is to give a complete derivation of the limiting distribution of large Frobenius numbers outlined in earlier work of J. Bourgain and Ya. Sinai and fill so…
Renewal-type Limit Theorem for the Gauss Map and Continued Fractions
Yakov G. Sinai, Corinna Ulcigrai
In this paper we prove the following renewal-type limit theorem. Given an irrational in (0,1) and R>0, let be the first denominator of the convergents of which ex…
A Limit Theorem for Birkoff sums of non-integrable functions over rotations
Yakov G. Sinai, Corinna Ulcigrai
We consider Birkhoff sums of functions with a singularity of type 1/x over rotations and prove the following limit theorem. Let be the N^th non-renormalized Birkhof…
Dynamics of a Massive Piston in an Ideal Gas
N. Chernov, J. L. Lebowitz, Ya. Sinai
We study a dynamical system consisting of a massive piston in a cubical container of large size filled with an ideal gas. The piston has mass and undergoes elastic…
Statistical (3x+1) -- problem
Yakov Sinai
Take an odd number x >0. Then 3x+1 is even and one can find an integer k> 0 so that y= 3x+1/2^k is again odd. We get in this way the mapping T, Tx=y. The paper contains two theorem…