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. 
@article{BUMI_2011_9_4_2_a1,
     author = {Bassetti, Federico and Gabetta, Ester},
     title = {Survey on {Probabilistic} {Methods} for the {Study} of {Kac-like} {Equations}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {187--212},
     publisher = {mathdoc},
     volume = {Ser. 9, 4},
     number = {2},
     year = {2011},
     zbl = {1229.60023},
     mrnumber = {2840602},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_2_a1/}
}
TY  - JOUR
AU  - Bassetti, Federico
AU  - Gabetta, Ester
TI  - Survey on Probabilistic Methods for the Study of Kac-like Equations
JO  - Bollettino della Unione matematica italiana
PY  - 2011
SP  - 187
EP  - 212
VL  - 4
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_2_a1/
LA  - en
ID  - BUMI_2011_9_4_2_a1
ER  - 
%0 Journal Article
%A Bassetti, Federico
%A Gabetta, Ester
%T Survey on Probabilistic Methods for the Study of Kac-like Equations
%J Bollettino della Unione matematica italiana
%D 2011
%P 187-212
%V 4
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_2_a1/
%G en
%F BUMI_2011_9_4_2_a1
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/