Asymptotic evolution in Kac's model

We consider the evolution equations for the moments of the distribution function in a probabilistic model due to Kac and called by him a caricature of the hard sphere dilute gas. We first discuss the characteristic time scales of the system. We then investigate the evolution equations for moments of a finite number of variables. Whatever the initial conditions, we show that asymptotically, i.e. when one considers only contributions depending on the longest characteristic time, these moments satisfy the condition of molecular chaos (in the linear approximation). The solution of these equations is a guide to find out the asymptotic solution of the exact evolution equations for all moments, including those involving O(N) variables.Hénin Françoise. Asymptotic evolution in Kac's model. In: Bulletin de la Classe des sciences, tome 60, 1974. pp. 686-720