We present a (mostly) rigorous approach to unbounded and bounded (open) dilute random Lorentz gases. Relying on previous rigorous results on the dilute (Boltzmann–Grad) limit we compute the asymptotics of the Lyapunov exponent in the unbounded case. For the bounded open case in a circular region we give an incomplete rigorous analysis which gives the asymptotics for large radius of the escape rate and of the rescaled ‘‘quasi-invariant’’ (q.i., or ‘‘quasistationary’’) measure. We finally give a complete proof on existence and asymptotic properties of the q.i. measure in a one-dimensional ‘‘caricature.’’
Some estimates for 2-dimensional infinite and bounded dilute random Lorentz gases / Boldrighini, Carlo; L. A., Bunimovich; A., Pellegrinotti. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 109:3-4(2002), pp. 729-745. [10.1023/a:1020470800432]
Some estimates for 2-dimensional infinite and bounded dilute random Lorentz gases
BOLDRIGHINI, Carlo;
2002
Abstract
We present a (mostly) rigorous approach to unbounded and bounded (open) dilute random Lorentz gases. Relying on previous rigorous results on the dilute (Boltzmann–Grad) limit we compute the asymptotics of the Lyapunov exponent in the unbounded case. For the bounded open case in a circular region we give an incomplete rigorous analysis which gives the asymptotics for large radius of the escape rate and of the rescaled ‘‘quasi-invariant’’ (q.i., or ‘‘quasistationary’’) measure. We finally give a complete proof on existence and asymptotic properties of the q.i. measure in a one-dimensional ‘‘caricature.’’I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.