HAL: hal-00294301, version 1

Detailed view

Export this paper BibTeX - EndNote - TEI - RefWorks -

Discrete and Continuous Dynamical Systems - Series A 21, 3 (2008) 729-747

LARGE DEVIATIONS FOR SHORT RECURRENCE

Miguel Abadi (  Corresponding author ) 1, Sandro Vaienti 2, 3

(2008-07-03)

Over a -mixing dynamical system we consider the function (Cn)/n in the limit of large n, where (Cn) is the first return of a cylinder of length n to itself. Saussol et al. ([30]) proved that this function is constant almost everywhere if the Cn are chosen in a descending sequence of cylinders around a given point. We prove upper and lower general bounds for its large deviation function. Under mild assumptions we compute the large deviation function directly and show that the limit corresponds to the R´enyi's entropy of the system. We finally compute the free energy function of (Cn)/n. We illustrate our results with a few examples.

1:	Instituto de Matem´atica, Estat´ıstica e Computa¸cˆao Cient´ıfica
	Universidade Estadual de Campinas; Bresil
2:	Centre de Physique Théorique (CPT)
	CNRS : FR2291 – Université de Provence - Aix-Marseille I – Université de la Méditerranée - Aix-Marseille II – Université Sud Toulon Var
3:	Fédération de Recherche des Unités de MAthématiques de Marseille (FRUMAM)
	CNRS : FR2291 – Université de Provence - Aix-Marseille I – Université de la Méditerranée - Aix-Marseille II – Université Paul Cézanne - Aix-Marseille III – Université Sud Toulon Var

Subject

:

Mathematics/Dynamical Systems

Keyword(s): Mixing – recurrence – overlapping – rare event – short correlation – large deviations

hal-00294301, version 1

http://hal.archives-ouvertes.fr/hal-00294301

oai:hal.archives-ouvertes.fr:hal-00294301

From: Sandro Vaienti <>

Submitted on: Wednesday, 9 July 2008 10:57:39

Updated on: Wednesday, 9 July 2008 11:12:59