We investigate large deviations for the empirical measure of the position and momentum of a particle traveling in a box with hot walls. The particle travels with uniform speed from left to right, until it hits the right boundary. Then it is absorbed and re-emitted from the left boundary with a new random speed, taken from an i.i.d. sequence. It turns out that this simple model, often used to model the interaction of a free particle with a heat bath, displays unusually complex large deviations features that we explain in detail. In particular, if the tail of the update distribution of the speed is sufficiently oscillating, then the empirical measure does not satisfy a large deviations principle, and we exhibit optimal lower and upper large deviations functionals.

Large deviations for a random speed particle / R., Lefevere; Mariani, Mauro; L., Zambotti. - In: ALEA. - ISSN 1980-0436. - STAMPA. - 9:2(2012), pp. 739-760.

Large deviations for a random speed particle

MARIANI, Mauro;
2012

Abstract

We investigate large deviations for the empirical measure of the position and momentum of a particle traveling in a box with hot walls. The particle travels with uniform speed from left to right, until it hits the right boundary. Then it is absorbed and re-emitted from the left boundary with a new random speed, taken from an i.i.d. sequence. It turns out that this simple model, often used to model the interaction of a free particle with a heat bath, displays unusually complex large deviations features that we explain in detail. In particular, if the tail of the update distribution of the speed is sufficiently oscillating, then the empirical measure does not satisfy a large deviations principle, and we exhibit optimal lower and upper large deviations functionals.
2012
renewal process; large deviations; heavy tails.; heavy tails
01 Pubblicazione su rivista::01a Articolo in rivista
Large deviations for a random speed particle / R., Lefevere; Mariani, Mauro; L., Zambotti. - In: ALEA. - ISSN 1980-0436. - STAMPA. - 9:2(2012), pp. 739-760.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/519561
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