Related papers: Hoeffding's inequality for sums of weakly dependen…

We show how to extend several basic concentration inequalities for simple random tensors $X = x_1 \otimes \cdots \otimes x_d$ where all $x_k$ are independent random vectors in $\mathbb{R}^n$ with independent coefficients. The new results…

Let $X,X_1,\ldots,X_n$ be independent identically distributed random variables. The paper deals with the question about the behavior of the concentration function of the random variable $\sum\limits_{k=1}^{n}X_k a_k$ according to the…

Using coupling techniques based on Stein's method for probability approximation, we revisit classical variance bounding inequalities of Chernoff, Cacoullos, Chen and Klaassen. Taking advantage of modern coupling techniques allows us to…

We present new explicit upper bounds for the smoothness of the distribution of the random diagonal sum $S_n=\sum_{j=1}^nX_{j,\pi(j)}$ of a random $n\times n$ matrix $X=(X_{j,r})$, where the $X_{j,r}$ are independent integer valued random…

This paper extends classical probabilistic results to the broader class of demimartingales and demisubmartingales. We establish variants of Doob's-type optional sampling theorem under minimal structural conditions on stopping times, relying…

We build optimal exponential bounds for the probabilities of large deviations of sums \sum_{k=1}^nf(X_k) where (X_k) is a finite reversible Markov chain and f is an arbitrary bounded function. These bounds depend only on the stationary mean…

In this paper we introduce and study the class of multivariate strong and strongly subexponential distributions. Some first properties are verified, as for example a type of multivariate analogue of Kesten's inequality, the closure property…

Let $\mathbf{W}=(W_1,W_2,...,W_k)$ be a random vector with nonnegative coordinates having nonzero and finite variances. We prove concentration inequalities for $\mathbf{W}$ using size biased couplings that generalize the previous univariate…

We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covariance. This nonasymptotic universality principle yields…

Given a large set $U$ where each item $a\in U$ has weight $w(a)$, we want to estimate the total weight $W=\sum_{a\in U} w(a)$ to within factor of $1\pm\varepsilon$ with some constant probability $>1/2$. Since $n=|U|$ is large, we want to do…

We show that the probability that a multilinear polynomial $f$ of independent random variables exceeds its mean by $\lambda$ is at most $e^{-\lambda^2 / (R^q Var(f))}$ for sufficiently small $\lambda$, where $R$ is an absolute constant.…

Let $(\xi_i)_{i=1,...,n}$ be a sequence of independent and symmetric random variables. We consider the upper bounds on tail probabilities of self-normalized deviations $$ \mathbf{P} \Big( \max_{1\leq k \leq n} \sum_{i=1}^{k} |\xi_i|\big/…

Let X_1 ,..., X_n be a collection of binary valued random variables and let f : {0,1}^n -> R be a Lipschitz function. Under a negative dependence hypothesis known as the {\em strong Rayleigh} condition, we show that f - E f satisfies a…

We consider the three dimensional array $\mathcal{A} = \{a_{i,j,k}\}_{1\le i,j,k \le n}$, with $a_{i,j,k} \in [0,1]$, and the two random statistics $T_{1}:= \sum_{i=1}^n \sum_{j=1}^n a_{i,j,\sigma(i)}$ and $T_{2}:= \sum_{i=1}^{n}…

Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers. In this paper, motived by the notion of independent and identically…

We explore negative dependence and stochastic orderings, showing that if an integer-valued random variable $W$ satisfies a certain negative dependence assumption, then $W$ is smaller (in the convex sense) than a Poisson variable of equal…

Hoeffding-type exponential inequalities are obtained for the distribution tails of canonical von Mises' statistics of arbitrary order based on samples from a stationary sequence of random variables satisfying the {\varphi}-mixing condition.…

Starting from concentration of measure hypotheses on $m$ random vectors $Z_1,\ldots, Z_m$, this article provides an expression of the concentration of functionals $\phi(Z_1,\ldots, Z_m)$ where the variations of $\phi$ on each variable…

Both complete decoupling and tangent decoupling are classical tools aiming to compare two random processes where one has a weaker dependence structure. We give a new proof for the complete decoupling inequality, which provides a lower bound…

In this paper, we establish Berry--Esseen bounds for both self-normalized and non-self-normalized sums of locally dependent random variables. The proofs are based on Stein's method together with a concentration inequality approach. We…