Geodesic
Survey on Probabilistic Methods for the Study of Kac-like Equations
Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 2, pp. 187-212.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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, are summarized. Finally, by resorting to the above mentioned probabilistic methods, some new results related to a linear kinetic model are proven. 
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Bassetti, Federico; Gabetta, Ester. Survey on Probabilistic Methods for the Study of Kac-like Equations. Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 2, pp. 187-212. http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_2_a1/

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