Related papers: Large deviations for equilibrium measures and sele…

We establish a Large Deviations Principle for stochastic processes with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof…

We consider $(M,d)$ a connected and compact manifold and we denote by $X$ the Bernoulli space $M^{\mathbb{N}}$. The shift acting on $X$ is denoted by $\sigma$. We analyze the general XY model, as presented in a recent paper by A. T.…

For $0\le \alpha <1$ and $\beta>2$, we consider a linear mod 1 transformation on a unit interval; $x\mapsto\beta x+\alpha$ (${\rm mod}\ 1$), and prove that it satisfies the level-2 large deviation principle with the unique measure of…

In this mainly survey paper we consider the Lagrangian $ L(x,v) = \frac{1}{2} \, |v|^2 - V(x) $, and a closed form $w$ on the torus $ \mathbb{T}^n $. For the associated Hamiltonian we consider the the Schrodinger operator ${\bf H}_\beta=\,…

We obtain an optimal deviation from the mean upper bound \begin{equation} D(x)\=\sup_{f\in \F}\mu\{f-\E_{\mu} f\geq x\},\qquad\ \text{for}\ x\in\R\label{abstr} \end{equation} where $\F$ is the class of the integrable, Lipschitz functions on…

Suppose $\alpha, \beta$ are Lipschitz strongly concave functions from $[0, 1]$ to $\mathbb{R}$ and $\gamma$ is a concave function from $[0, 1]$ to $\mathbb{R}$, such that $\alpha(0) = \gamma(0) = 0$, and $\alpha(1) = \beta(0) = 0$ and…

Suppose $\sigma$ is the shift acting on Bernoulli space $X=\{0,1\}^\mathbb{N}$, and, consider a fixed function $f:X \to \mathbb{R}$, under the Waters's conditions (defined in a paper in ETDS 2007). For each real value $t\geq 0$ we consider…

We study large deviations for measurable averaging operators on state spaces of dynamical systems. Our main motivation is the Hecke operators on the modular curve Y_0(p^n) and their generalization to higher rank S-arithmetic quotients. We…

We consider finite $\beta$-ensembles $\mathcal X_{n,\beta}^{\mathbb F}$ with $n$ points on $\mathbb F$, where $\mathbb F$ denotes either the real line or the complex plane. Let $U$ be a bounded subset of $ \mathbb F$ such that $\partial U$…

We establish large deviation principles (LDPs) for empirical measures associated with a sequence of Gibbs distributions on $n$-particle configurations, each of which is defined in terms of an inverse temperature $% \beta_n$ and an energy…

In this paper we prove a large deviation principle for the empirical drift of a one-dimensional Brownian motion with self-repellence called the Edwards model. Our results extend earlier work in which a law of large numbers, respectively, a…

Consider $\beta > 1$ and $\lfloor \beta \rfloor$ its integer part. It is widely known that any real number $\alpha \in \Bigl[0, \frac{\lfloor \beta \rfloor}{\beta - 1}\Bigr]$ can be represented in base $\beta$ using a development in series…

We consider discrete $\beta$-ensembles, as introduced by Borodin, Gorin and Guionnet in (Publications math{\' e}matiques de l'IH{\' E}S 125, 1-78, 2017). Under general assumptions, we establish a large deviation principle for the empirical…

This paper explores the equivalences between four definitions of uniform large deviations principles and uniform Laplace principles found in the literature. Counterexamples are presented to illustrate the differences between these…

Let L be a positive line bundle over a projective complex manifold X. Consider the space of holomorphic sections of the tensor power of order p of L. The determinant of a basis of this space, together with some given probability measure on…

In this note we prove the following good-$\lambda$ inequality, for $r>2$, all $\lambda > 0$, $\delta \in \big(0, \frac{1}{2} \big)$ \[ \nu\big\{ V_r(f) > 3 \lambda ; \mathcal{M}(f) \leq \delta \lambda\big\} \leq 4 \nu\{s(f) > \delta…

We establish large deviations estimates for the largest eigenvalue of Wigner matrices with sub-Gaussian entries. Under technical assumptions, we show that the large deviation behavior of the largest eigenvalue is universal for small…

For any hyperbolic rational map and any net of Borel probability measures on the space of Borel probability measures on the Julia set, we show that this net satisfies a strong form of the large deviation principle with a rate function given…

Let $\Sigma_{A}(\mathbb{N})$ be a topologically mixing countable Markov shift with the BIP property over the alphabet $\mathbb{N}$ and $f: \Sigma_{A}(\mathbb{N}) \rightarrow \mathbb{R}$ a potential satisfying the Walters condition with…

We consider the Gaussian beta-ensemble when $\beta$ scales with $n$ the number of particles such that $\displaystyle{{n}^{-1}\ll \beta\ll 1}$. Under a certain regime for $\beta$, we show that the largest particle satisfies a large…