Related papers: Concentration inequalities via zero bias couplings

We are interested in Sobolev type inequalities and their relationship with concentration properties on higher dimensions. We consider unbounded spin systems on the d-dimensional lattice with interactions that increase slower than a…

We present conditions that allow us to pass from the convergence of probability measures in distribution to the uniform convergence of the associated quantile functions. Under these conditions, one can in particular pass from the asymptotic…

We introduce a one dimensional disordered Ising model which at zero temperature is characterized by a non-trivial, non-self-averaging, overlap probability distribution when the impurity concentration vanishes in the thermodynamic limit. The…

Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product $XY$ is derived. Some basic distributional properties are also derived, including…

For a real-valued measurable function $f$ and a nonnegative, nondecreasing function $\phi$, we first obtain a Chebyshev type inequality which provides an upper bound for $\displaystyle \phi(\lambda_{1}) \mu(\{x \in \Omega : f(x) \geq…

Let $\BS_1,...,\BS_n$ be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter $p\in(0,1)$. Let $m_*(p):=(1+p+2p^2)/(2\sqrt{p-p^2}+4p^2)$ if $0<p\le 1/2$ and $m_*(p):=1$ if…

We study the exact constants in the moment inequalities for sums of centered independent random variables: improve their asymptotics, low and upper bounds, calculate more exact asymptotics, elaborate the numerical algorithm for their…

Let $X_1,\ldots,X_M$ and $Y_1,\ldots,Y_N$ be independent zero mean normal random variables with variances $\sigma_{X_i}^2$, $i=1,\ldots,M$, and $\sigma_{Y_j}^2$, $j=1,\ldots,N$, respectively, and let $X=X_1\cdots X_M$ and $Y=Y_1\cdots Y_N$.…

In this paper, we generalize and improve some fundamental concentration inequalities using information on the random variables' higher moments. In particular, we improve the classical Hoeffding's and Bennett's inequalities for the case…

For a sequence $\{X_{n}, \, n \geqslant 1 \}$ of nonnegative random variables where $\max[\min(X_{n} - s,t),0]$, $t > s \geqslant 0$, satisfy a moment inequality, sufficient conditions are given under which $\sum_{k=1}^n (X_k - \mathbb{E}…

In this paper, we propose a new distribution over the unit interval which can be characterized as a ratio of the type $Z=Y/(X+Y)$ where $X$ and $Y$ are two correlated Birnbaum-Saunders random variables. The density of $Z$ may be unimodal or…

The concentration of measure phenomenon in Gauss' space states that every $L$-Lipschitz map $f$ on $\mathbb R^n$ satisfies \[ \gamma_{n} \left(\{ x : | f(x) - M_{f} | \geqslant t \} \right) \leqslant 2 e^{ - \frac{t^2}{ 2L^2} }, \quad t>0,…

The goal of this article is two-fold: in a first part, we prove Azuma-Hoeffding type concentration inequalities around the drift for the displacement of non-elementary random walks on hyperbolic spaces. For a proper hyperbolic space $M$, we…

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 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…

Anomaly matching constrains low-energy physics of strongly-coupled field theories, but it is not useful at finite temperature due to contamination from high-energy states. The known exception is an 't Hooft anomaly involving one-form…

We characterize the symmetric distributions that can be (approximately) generated by shallow Boolean circuits. More precisely, let $f\colon \{0,1\}^m \to \{0,1\}^n$ be a Boolean function where each output bit depends on at most $d$ input…

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…

The collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied when the natural frequency distribution does not possess an even symmetry with respect to the average natural frequency…

We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…