相关论文: Some deviation inequalities
This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…
We investigate small deviation properties of Gaussian random fields in the space $L_q(\R^N,\mu)$ where $\mu$ is an arbitrary finite compactly supported Borel measure. Of special interest are hereby "thin" measures $\mu$, i.e., those which…
Recently, financial industry and regulators have enhanced the debate on the good properties of a risk measure. A fundamental issue is the evaluation of the quality of a risk estimation. On the one hand, a backtesting procedure is desirable…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
We establish a universal framework for concentration inequalities based on invariance under diffeomorphism groups. Given a probability measure $\mu$ on a space $E$ and a diffeomorphism $\psi: E \to F$, concentration properties transfer…
We prove concentration inequalities for general functions of weakly dependent random variables satisfying the Dobrushin condition. In particular, we show Talagrand's convex distance inequality for this type of dependence. We apply our…
We start providing a quantitative stability theorem for the rigidity of an overdetermined problem involving harmonic functions in a punctured domain. Our approach is inspired by and based on the proof of rigidity established by Enciso and…
While classical concentration inequalities are typically restricted to two special cases -- independence and martingale difference sequences -- we extend concentration inequalities to a much broader class of stochastic processes by relaxing…
This paper studies the concentration properties of random codes. Specifically, we show that, for discrete memoryless channels, the error exponent of a randomly generated code with pairwise-independent codewords converges in probability to…
We use the generic chaining device proposed by Talagrand to establish exponential bounds on the deviation probability of some suprema of random processes. Then, given a random vector $\xi$ in $\R^{n}$ the components of which are independent…
Stein's method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this paper, we provide some extensions of the…
We initiate a study of a new model of property testing that is a hybrid of testing properties of distributions and testing properties of strings. Specifically, the new model refers to testing properties of distributions, but these are…
This article exists first and foremost to contribute to a tribute to Patrick Cattiaux. One of the two authors has known Patrick Cattiaux for a very long time, and owes him a great deal. If we are to illustrate the adage that life is made up…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
Recent dispersive techniques developed by us are applied to discuss three problems: 1. A long standing discrepan-cy between the measurements of $R(s)$ for $\sqrt{s} = (5\div 7.5)GeV$ by Crystal Ball and MARK I has been analyzed and its…
We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these…
For a large class of random matrices $A$ with i.i.d. entries we show that the $\ell_1$-quotient property holds with probability exponentially close to 1. In contrast to previous results, our analysis does not require concentration of the…
This paper presents compact notations for concentration inequalities and convenient results to streamline probabilistic analysis. The new expressions describe the typical sizes and tails of random variables, allowing for simple operations…
We give a characterization of transport-entropy inequalities in metric spaces. As an application we deduce that such inequalities are stable under bounded perturbation (Holley-Stroock perturbation Lemma).
We investigate a family of distributions having a property of stability-under-addition, provided that the number $\nu$ of added-up random variables in the random sum is also a random variable. We call the corresponding property a…