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 0, converges to a specific Maxwellian distribution if and only if the second absolute moment is finite, with respect to the total variation distance. The problem of finding the optimal 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.