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Sur un critère de récurrence en dimension 2 pour les marches stationnaires, applications

Published online by Cambridge University Press:  01 October 1999

J.-P. CONZE
Affiliation:
Université de Rennes I, Campus de Beaulieu, 35042, Rennes Cedex, France

Abstract

Let $(E,{\cal A},\mu,T)$ be a dynamical system and let $\Phi$ be a function defined on $E$ with values in $\mathbb{R}^2$. We give a criterion, the central limit theorem along subsequences of positive density, for the recurrence of the corresponding ‘stationary walk’ defined as the cocycle $\big(\sum^{n-1}_{j=0}\Phi(T^jx)\big)_{n\geq1}$.

This criterion is satisfied by functions which are homologous to a martingale difference (a property which holds for regular functions in many systems). It can also be applied to the periodic Lorentz gas in the plane and shows recurrence for this model.

Type
Research Article
Copyright
1999 Cambridge University Press

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