Sharp large deviations for hyperbolic flows
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PETKOV, Vesselin | |
| hal.structure.identifier | The University of Western Australia [UWA] | |
| dc.contributor.author | STOYANOV, Luchezar | |
| dc.date.accessioned | 2024-04-04T02:55:48Z | |
| dc.date.available | 2024-04-04T02:55:48Z | |
| dc.date.created | 2020-11-10 | |
| dc.date.issued | 2020 | |
| dc.identifier.issn | 1424-0637 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192398 | |
| dc.description.abstractEn | For hyperbolic flows $\varphi_t$ we examine the Gibbs measure of points $w$ for which $$\int_0^T G(\varphi_t w) dt - a T \in (- e^{-\epsilon n}, e^{- \epsilon n})$$ as $n \to \infty$ and $T \geq n$, provided $\epsilon > 0$ is sufficiently small. This is similar to local central limit theorems. The fact that the interval $(- e^{-\epsilon n}, e^{- \epsilon n})$ is exponentially shrinking as $n \to \infty$ leads to several difficulties. Under some geometric assumptions we establish a sharp large deviation result with leading term $C(a) \epsilon_n e^{\gamma(a) T}$ and rate function $\gamma(a) \leq 0.$ The proof is based on the spectral estimates for the iterations of the Ruelle operators with two complex parameters and on a new Tauberian theorem for sequence of functions $g_n(t)$ having an asymptotic as $ n \to \infty$ and $t \geq n.$ | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.subject.en | hyperbolic flows | |
| dc.subject.en | large deviations | |
| dc.subject.en | Tauberian theorem for sequence of functions | |
| dc.title.en | Sharp large deviations for hyperbolic flows | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00023-020-00956-8 | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 2002.11007v3 | |
| bordeaux.journal | Annales Henri Poincaré | |
| bordeaux.page | 3791-3834 | |
| bordeaux.volume | 21 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 12 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02498740 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02498740v1 | |
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