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On random almost periodic series and random ergodic theory

Published online by Cambridge University Press:  01 June 2006

GUY COHEN  and
CHRISTOPHE CUNY
GUY COHEN
Affiliation:
Erwin Schrödinger Institute for Mathematical Physics (ESI), Vienna, Austria (e-mail: gc@math.huji.ac.il) the Hebrew University of Jerusalem, Israel
CHRISTOPHE CUNY
Affiliation:
University of New-Caledonia, Equipe, ERIM, Noumea, New-Caledonia (e-mail: cuny@univ-nc.nc)
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Abstract

In this paper we obtain different types of random ergodic theorems for dynamical systems or continuous semi-flows. These results recover and extend previous works on dynamical systems and are completely new in the case of semi-flows. The proofs are based on uniform estimates on random almost periodic polynomials that we obtained very recently and on an improvement of a tool introduced by Talagrand in 1995 and further developed by Fernique in 1996. In the course of this, we partially recover results of Marcus and Pisier from the 1980s on almost sure uniform convergence of random almost periodic series.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 3 , June 2006 , pp. 683 - 709
Copyright
2006 Cambridge University Press

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