We consider a mechanical system in the plane, consisting of a vertical rod of length l, with its center moving on the horizontal axis, subject to elastic collisions with the particles of a free gas, and to a constant force f. Assuming a suitable initial measure we show that the evolution of the system as seen from the rod is described by an exponentially ergodic irreducible Harris chain, implying convergence to a stationary invariant measure as t goes to + oo. We deduce that in the proper scaling the motion of the rod is described as a drift plus a diffusion. We prove in conclusion that the diffusion is nondegenerate and that the drift is nonzero if f\neq 0 and has the same sign of f.

DRIFT AND DIFFUSION FOR A MECHANICAL SYSTEM / Boldrighini, Carlo; M., Soloveichik. - In: PROBABILITY THEORY AND RELATED FIELDS. - ISSN 0178-8051. - STAMPA. - 103:3(1995), pp. 349-379. [10.1007/bf01195479]

DRIFT AND DIFFUSION FOR A MECHANICAL SYSTEM

BOLDRIGHINI, Carlo;
1995

Abstract

We consider a mechanical system in the plane, consisting of a vertical rod of length l, with its center moving on the horizontal axis, subject to elastic collisions with the particles of a free gas, and to a constant force f. Assuming a suitable initial measure we show that the evolution of the system as seen from the rod is described by an exponentially ergodic irreducible Harris chain, implying convergence to a stationary invariant measure as t goes to + oo. We deduce that in the proper scaling the motion of the rod is described as a drift plus a diffusion. We prove in conclusion that the diffusion is nondegenerate and that the drift is nonzero if f\neq 0 and has the same sign of f.
1995
diffusion; infinite particle systems; stationary non-equilibrium states
01 Pubblicazione su rivista::01a Articolo in rivista
DRIFT AND DIFFUSION FOR A MECHANICAL SYSTEM / Boldrighini, Carlo; M., Soloveichik. - In: PROBABILITY THEORY AND RELATED FIELDS. - ISSN 0178-8051. - STAMPA. - 103:3(1995), pp. 349-379. [10.1007/bf01195479]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/28305
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