### Rutgers Discrete Mathematics Seminar

Title: Where does randomness come from?

subtitle: Deterministic approach to the kinetic theory of gases

Speaker: **Jozsef Beck**, Rutgers University

Date: Thursday, March 25, 2010 2:00pm

Location: Hill Center, Room 525, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:
The classical Bernoulli model describes gases as a large system of point-billiards (in the range of 10^{23}) in a cube container, where the particles move with constant speed, and the collision against the walls are according to the law of elastic reflection (i.e., the angle of incidence equals the angle of reflection). We prove that, under typical initial conditions (i.e., typical initial position of the particles, and typical velicity distribution), the long-term time-evolution of the system exhibits textbook randomness. We prove, among others, a ``local" Poisson Law, and a ``global"
central limit theorem. These results justify the postulate of statistical mechanics that the particles are represented by random variables. In spite of the fact that ``we just prove what is expected", there are many surprises here. (Perhaps the biggest surprise is why people didn't prove these results, say, 60-80 years ago.)