Rapidity of convergence to equilibrium of the solution of the Boltzmann equation for Maxwellian molecules

The paper reviews some results, recently presented in [2], concerning the asymptotic behavior of solutions of the homogeneous Boltzmann equation for Maxwellian molecules. It is well-known that the solution to this equation, given an initial datum μ0, converges to a specific Maxwellian distribution if and only if 3 |x|2μ0(dx) is finite, with respect to the total variation distance. The problem of finding the optimal R bound for the distance between the solution at time t and the equilibrium, proposed about one hundred years ago, is solved in [2] by using techniques of a probabilistic nature, linked with the central limit theorem.