Related papers: A concentration inequality for product spaces
We give a concentration inequality based on the premise that random variables take values within a particular region. The concentration inequality guarantees that, for any sequence of correlated random variables, the difference between the…
We present a non-asymptotic concentration inequality for the random matrix product \begin{equation}\label{eq:Zn} Z_n = \left(I_d-\alpha X_n\right)\left(I_d-\alpha X_{n-1}\right)\cdots \left(I_d-\alpha X_1\right), \end{equation} where…
Concentration inequalities quantify the deviation of a random variable from a fixed value. In spite of numerous applications, such as opinion surveys or ecological counting procedures, few concentration results are known for the setting of…
We present a proof of the concentration inequality for a discrete random surface model, where the underlying potential is perturbed by an additive random potential. The proof is based on annealing the random potential, and follows the…
In this note we derive a sharp concentration inequality for the supremum of a smooth random field over a finite dimensional set. It is shown that this supremum can be bounded with high probability by the value of the field at some…
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…
The concentration of measure prenomenon roughly states that, if a set $A$ in a product $\Omega^N$ of probability spaces has measure at least one half, ``most'' of the points of $\Omega^N$ are ``close'' to $A$. We proceed to a systematic…
We explore the question whether Lipschitz functions of random variables under various forms of negative correlation satisfy concentration bounds similar to McDiarmid's inequality for independent random variables. We prove such a…
If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish concentration inequalities for finite sequences of…
We consider a random variable $X$ that takes values in a (possibly infinite-dimensional) topological vector space $\mathcal{X}$. We show that, with respect to an appropriate "normal distance" on $\mathcal{X}$, concentration inequalities for…
We show that for any metric probability space $(M,d,\mu)$ with a subgaussian constant $\sigma^2(\mu)$ and any set $A \subset M$ we have $\sigma^2(\mu_A) \leq c \log\left(e/\mu(A)\right)\,\sigma^2(\mu)$, where $\mu_A$ is a restriction of…
We prove concentration inequalities for functions of independent random variables {under} sub-gaussian and sub-exponential conditions. The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher…
In this paper we revisit Talagrand's proof of concentration inequality for empirical processes. We give a different shorter proof of the main technical lemma that guarantees the existence of a certain kernel. Our proof provides the almost…
We extend recent higher order concentration results in the discrete setting to include functions of possibly dependent variables whose distribution (on the product space) satisfies a logarithmic Sobolev inequality with respect to a…
We investigate concentration inequalities for Dirichlet and Multinomial random variables.
Concentration inequalities are fundamental tools in probabilistic combinatorics and theoretical computer science for proving that random functions are near their means. Of particular importance is the case where f(X) is a function of…
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…
For a stochastic process with state space some Polish space, this paper gives sufficient conditions on the initial and conditional distributions for the joint law to satisfy Gaussian concentration inequalities, transportation inequalities…
In this work we design a general method for proving moment inequalities for polynomials of independent random variables. Our method works for a wide range of random variables including Gaussian, Boolean, exponential, Poisson and many…
Initially motivated by the study of the non-asymptotic properties of non-parametric tests based on permutation methods, concentration inequalities for uniformly permuted sums have been largely studied in the literature. Recently, Delyon et…