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Given Holder continuous functions $f$ and $psi$ on a sub-shift of finite type $Sigma_A^{+}$ such that $psi$ is not cohomologous to a constant, the classical large deviation principle holds (cite{OP}, cite{Kif}, cite{Y}) with a rate function $I_psigeq 0$ such that $I_psi (p) = 0$ iff $p = int psi , d mu$, where $mu = mu_f$ is the equilibrium state of $f$. In this paper we derive a uniform estimate from below for $I_psi$ for $p$ outside an interval containing $tilde{psi} = int psi , dmu$, which depends only on the sub-shift, the function $f$, the norm $|psi|_infty$, the Holder constant of $psi$ and the integral $tilde{psi}$. Similar results can be derived in the same way e.g. for Axiom A diffeomorphisms on basic sets.
For an arbitrary negative Schwarzian unimodal map with non-flat critical point, we establish the level-2 Large Deviation Principle (LDP) for empirical distributions. We also give an example of a multimodal map for which the level-2 LDP does not hold.
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 simila
We give an exponential upper bound on the probabilitywith which the denominator of the $n$th convergent in the regular continued fraction expansion stays away from the mean $frac{npi^2}{12log2}$. The exponential rate is best possible, given by an ana
We study equidistribution properties of translations on nilmanifolds along functions of polynomial growth from a Hardy field. More precisely, if $X=G/Gamma$ is a nilmanifold, $a_1,ldots,a_kin G$ are commuting nilrotations, and $f_1,ldots,f_k$ are fun
We construct a stochastic model showing the relationship between noise, gradient flows and rate-independent systems. The model consists of a one-dimensional birth-death process on a lattice, with rates derived from Kramers law as an approximation of