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.’’
2002
boltzmann-grad limit; lorentz gas; lyapunov exponents; quasi-stationary measures
01 Pubblicazione su rivista::01a Articolo in rivista
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/28310
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