From Rates of mixing to recurrence times via large deviations
| Autor: | Sandro Vaienti, José F. Alves, Jorge Milhazes Freitas, Stefano Luzzatto |
|---|---|
| Přispěvatelé: | Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
Discrete mathematics
Mathematics(all) Dynamical systems theory Decay of correlations General Mathematics 010102 general mathematics [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] Dynamical Systems (math.DS) 01 natural sciences 010104 statistics & probability Large deviations Gibbs–Markov structure Mixing (mathematics) FOS: Mathematics Piecewise Large deviations theory Statistical physics Mathematics - Dynamical Systems 0101 mathematics Invariant (mathematics) Mathematics |
| Zdroj: | Advances in Mathematics Advances in Mathematics, 2011, 228 (2), pp.1203-1230. ⟨10.1016/j.aim.2011.06.014⟩ Advances in Mathematics, Elsevier, 2011, 228, pp.1203-1230 |
| ISSN: | 0001-8708 1090-2082 |
| DOI: | 10.1016/j.aim.2011.06.014⟩ |
| Popis: | International audience; A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of correlations. Such geometric structures are generally highly non-trivial and thus a natural question is the extent to which this approach can be applied. In this paper we show that in many cases stochastic-like behaviour itself implies that the system has certain non-trivial geometric properties, which are therefore necessary as well as sufficient conditions for the occurrence of the statistical properties under consideration. As a by product of our techniques we also obtain some new results on large deviations for certain classes of systems which include Viana maps and multidimensional piecewise expanding maps. |
| Databáze: | OpenAIRE |
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