تقرير
Probabilistic View of Explosion in an Inelastic Kac Model
| العنوان: | Probabilistic View of Explosion in an Inelastic Kac Model |
|---|---|
| المؤلفون: | Bonomi, Andrea, Perversi, Eleonora, Regazzini, Eugenio |
| سنة النشر: | 2013 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability, 60F05, 82C40, 60B10 |
| الوصف: | Let $\{\mu(\cdot,t):t\geq0\}$ be the family of probability measures corresponding to the solution of the inelastic Kac model introduced in Pulvirenti and Toscani [\textit{J. Stat. Phys.} \textbf{114} (2004) 1453-1480]. It has been proved by Gabetta and Regazzini [\textit{J. Statist. Phys.} \textbf{147} (2012) 1007-1019] 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 $-\infty$ and probability 1/2 "adherent" to $+\infty$. 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. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s10955-014-0921-2 |
| URL الوصول: | http://arxiv.org/abs/1306.0691 |
| رقم الأكسشن: | edsarx.1306.0691 |
| قاعدة البيانات: | arXiv |
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