Survey on Probabilistic Methods for the Study of Kac-like Equations
This mainly explanatory paper shows how direct application of probabilistic methods, pertaining to central limit general theory, can enlighten us about the relaxation to equilibrium of the solutions of one-dimensional Boltzmann type equations. In particular, conditions under which the solutions of these equations converge to suitable scale mixture of stable distributions are reviewed. In addition, some recent results about the rate of convergence to steady states, with respect to various metrics,...