Related papers: A note on Talagrand's convex hull concentration in…
We give a sufficient condition for the exponential decay of the tail probability of a non-negative random variable. We consider the Laplace-Stieltjes transform of the probability distribution function of the random variable. We present a…
This paper is the Part II of a serious work about T product tensors focusing at establishing new probability bounds for sums of random, independent, T product tensors. These probability bounds characterize large deviation behavior of the…
In a large, possibly infinite population, each subject is colored red with probability $p$, independently of the others. Then, a finite sub-population is selected, possibly as a function of the coloring. The imbalance in the sub-population…
In this paper we present various new inequalities for tail proabilities for distributions that are elements of the most improtant exponential families. These families include the Poisson distributions, the Gamma distributions, the binomial…
Talagrand's fundamental result on the entropy numbers is slightly improved. Our proof uses different ideas based on results from greedy approximation.
The inequality of Clauser and Horne [ Phys. Rev. D 10, 526 (1974)], intended to overcome the limited scope of other inequalities to deterministic theories, is shown to have a resticted validity even in case of perfect detectors and perfect…
We present some extensions of Bernstein's concentration inequality for random matrices. This inequality has become a useful and powerful tool for many problems in statistics, signal processing and theoretical computer science. The main…
For a $d$-dimensional random vector $X$, let $p_{n, X}(\theta)$ be the probability that the convex hull of $n$ independent copies of $X$ contains a given point $\theta$. We provide several sharp inequalities regarding $p_{n, X}(\theta)$ and…
An explicit upper bound on the tail probabilities for the normalized Rademacher sums is given. This bound, which is best possible in a certain sense, is asymptotically equivalent to the corresponding tail probability of the standard normal…
In this paper, we provide an alternative proof of Donaldson's almost-holomorphic section theorem and symplectic Lefschetz pencil theorem, through constructions of certain special kind of Donaldson-type sections of the line bundle based on…
The authors announce a general tail estimate, called a decoupling inequality, for a symmetrized sum of non-linear $k$-correlations of $n>k$ independent random variables.
In this work, we investigate the question of how knowledge about expectations $\mathbb{E}(f_i(X))$ of a random vector $X$ translate into inequalities for $\mathbb{E}(g(X))$ for given functions $f_i$, $g$ and a random vector $X$ whose…
Concentration inequalities for subgraph counts in random geometric graphs built over Poisson point processes are proved. The estimates give upper bounds for the probabilities $\mathbb{P}(N\geq M +r)$ and $\mathbb{P}(N\leq M - r)$ where $M$…
The paper deals with studying a connection of the Littlewood--Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions.
We establish concentration inequalities in the class of ultra log-concave distributions. In particular, we show that ultra log-concave distributions satisfy Poisson concentration bounds. As an application, we derive concentration bounds for…
Proving a conjecture of Talagrand, a fractional version of the 'expectation-threshold' conjecture of Kalai and the second author, we show for any increasing family $F$ on a finite set $X$ that $p_c (F) =O( q_f (F) \log \ell(F))$, where…
Sums of independent, bounded random variables concentrate around their expectation approximately as well a Gaussian of the same variance. Well known results of this form include the Bernstein, Hoeffding, and Chernoff inequalities and many…
This note is concerned with concentration inequalities for extrema of stationary Gaussian processes. It provides non-asymptotic tail inequalities which fully reflect the fluctuation rate, and as such improve upon standard Gaussian…
We prove a version of Talagrand's concentration inequality for subordinated sub-Laplacian on a compact Riemannian manifold using tools from noncommutative geometry. As an application, motivated by quantum information theory, we show that on…
Let f be a stationary isotropic non-degenerate Gaussian field on R^2. Assume that f = q * W where q is both C^2 and L^2 and W is the L^2 white noise on R^2. We extend a result by Stephen Muirhead and Hugo Vanneuville by showing that,…