Probabilistic View of Explosion in an Inelastic Kac Model (Articolo in rivista)

Type
Label
  • Probabilistic View of Explosion in an Inelastic Kac Model (Articolo in rivista) (literal)
Anno
  • 2014-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1007/s10955-014-0921-2 (literal)
Alternative label
  • Bonomi, Andrea; Perversi, Eleonora; Regazzini, Eugenio (2014)
    Probabilistic View of Explosion in an Inelastic Kac Model
    in Journal of statistical physics; Springer US, Boston (Stati Uniti d'America)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Bonomi, Andrea; Perversi, Eleonora; Regazzini, Eugenio (literal)
Pagina inizio
  • 1292 (literal)
Pagina fine
  • 1324 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://link.springer.com/article/10.1007/s10955-014-0921-2 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 154 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#pagineTotali
  • 33 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 5 (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • University of Pavia; Consiglio Nazionale delle Ricerche (CNR) (literal)
Titolo
  • Probabilistic View of Explosion in an Inelastic Kac Model (literal)
Abstract
  • Let {mu(., t) : t >= 0} be the family of probability measures corresponding to the solution of the inelastic Kac model introduced in Pulvirenti and Toscani (J Stat Phys 114: 1453-1480, 2004). It has been proved by Gabetta and Regazzini (J Stat Phys 147: 10071019, 2012) that the solution converges weakly to equilibrium if and only if a suitable symmetrized form of the initial data belongs to the standard domain of attraction of a specific stable law. In the present paper it is shown that, for initial data which are heavier-tailed than the aforementioned ones, the limiting distribution is improper in the sense that it has probability 1/2 \"adherent\" to -infinity and probability 1/2 \"adherent\" to +infinity. It is explained in which sense this phenomenon is amenable to a sort of explosion, and the main result consists in an explicit expression of the rate of such an explosion. The presentation of these statements is preceded by a discussion about the necessity of the assumption under which their validity is proved. This gives the chance to make an adjustment to a portion of a proof contained in the above-mentioned paper by Gabetta and Regazzini. (literal)
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