Survey on Probabilistic Methods for the Study of Kac-like Equations
Bassetti, Federico ; Gabetta, Ester
Bollettino dell'Unione Matematica Italiana, Tome 4 (2011), p. 187-212 / Harvested from Biblioteca Digitale Italiana di Matematica
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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.

Publié le : 2011-06-01
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     author = {Federico Bassetti and Ester Gabetta},
     title = {Survey on Probabilistic Methods for the Study of Kac-like Equations},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {4},
     year = {2011},
     pages = {187-212},
     zbl = {1229.60023},
     mrnumber = {2840602},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2011_9_4_2_187_0}
}

Bassetti, Federico; Gabetta, Ester. Survey on Probabilistic Methods for the Study of Kac-like Equations. Bollettino dell'Unione Matematica Italiana, Tome 4 (2011) pp. 187-212. http://gdmltest.u-ga.fr/item/BUMI_2011_9_4_2_187_0/

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