The system will be going down for regular maintenance. Please save your work and logout.
Sharp large deviations for hyperbolic flows
Language
en
Article de revue
This item was published in
Annales Henri Poincaré. 2020, vol. 21, n° 12, p. 3791-3834
Springer Verlag
English Abstract
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 > ...Read more >
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 $t \geq n.$Read less <
English Keywords
hyperbolic flows
large deviations
Tauberian theorem for sequence of functions
Origin
Hal imported