Related papers: Concentration on the Boolean hypercube via pathwis…

Let $I, J\subset \mathbb{R}$ be closed intervals, and let $H$ be $C^{3}$ smooth real valued function on $I\times J$ with nonvanishing $H_{x}$ and $H_{y}$. Take any fixed positive numbers $a,b$, and let $d\mu$ be a probability measure with…

Inference on vertex-aligned graphs is of wide theoretical and practical importance.There are, however, few flexible and tractable statistical models for correlated graphs, and even fewer comprehensive approaches to parametric inference on…

A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is given here. In the case of the variational method, the Bogoliubov inequality is generalized in a very…

In the paper we pursue the analysis from the section 5 of the Talagrand's paper "Sample boundedness of stochastic processes under increment conditions." Ann. Probab. 18, No. 1, 1-49. In particular we give the proof of some Sobolev…

We prove concentration inequalities for $f\left( X\right) $ about its median, where $X$ is a random vector in $\mathbb{R}^n$ with independent heavy tailed coordinates of Weibull or power type, and $f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a…

In this article we continue our investigation of the thin obstacle problem with variable coefficients which was initiated in \cite{KRS14}, \cite{KRSI}. Using a partial Hodograph-Legendre transform and the implicit function theorem, we prove…

It is shown that functions defined on $\{0,1,...,r-1\}^n$ satisfying certain conditions of bounded differences that guarantee sub-Gaussian tail behavior also satisfy a much stronger ``local'' sub-Gaussian property. For self-bounding and…

The influence of the $k$'th coordinate on a Boolean function $f:\{0,1\}^n \rightarrow \{0,1\}$ is the probability that flipping $x_k$ changes the value $f(x)$. The total influence $I(f)$ is the sum of influences of the coordinates. The…

Let $\mathbb{H}^{n}=\mathbb{C}^{n}\times\mathbb{R}$ be the $n$-dimensional Heisenberg group, $Q=2n+2$ be the homogeneous dimension of $\mathbb{H}^{n}$. We extend the well-known concentration-compactness principle on finite domains in the…

The Fourier Entropy-Influence (FEI) Conjecture of Friedgut and Kalai states that ${\bf H}[f] \leq C \cdot {\bf I}[f]$ holds for every Boolean function $f$, where ${\bf H}[f]$ denotes the spectral entropy of $f$, ${\bf I}[f]$ is its total…

This paper establishes quantitative Carleman-type inequalities for holomorphic sections of Hermitian vector bundles over bounded domains in $\mathbb{C}^n$ with $n \geq 2$. We first prove a Sobolev-type inequality with explicit constants for…

We consider square-integrable functionals of Poisson point processes for which the variance upper bound provided by the classical Poincar\'{e} inequality is suboptimal, a phenomenon known as superconcentration. In this paper, we establish a…

The problem of testing monotonicity for Boolean functions on the hypergrid, $f:[n]^d \to \{0,1\}$ is a classic topic in property testing. When $n=2$, the domain is the hypercube. For the hypercube case, a breakthrough result of…

We prove generalised concentration inequalities for a class of scaled self-bounding functions of independent random variables, referred to as ${(M,a,b)}$ self-bounding. The scaling refers to the fact that the component-wise difference is…

We study nonparametric distance-based (isotropic) local polynomial methods for estimating the boundary average treatment effect curve, a causal functional that captures treatment effect heterogeneity in boundary discontinuity designs. We…

We show that the Bernstein-Hoeffding method can be employed to a larger class of generalized moments. This class includes the exponential moments whose properties play a key role in the proof of a well-known inequality of Wassily Hoeffding,…

The paper reexamines an argument by Talagrand that leads to a remarkable exponential tail bound for the concentration of probability near a set. The main novelty is the replacement of a mysterious Calculus inequality by an application of…

We consider the problem of minimizing a given $n$-variate polynomial $f$ over the hypercube $[-1,1]^n$. An idea introduced by Lasserre, is to find a probability distribution on $[-1,1]^n$ with polynomial density function $h$ (of given…

In this article we derive Talagrand's $T_2$ inequality on the path space w.r.t. the maximum norm for various stochastic processes, including solutions of one-dimensional stochastic differential equations with measurable drifts, backward…

Under the Ornstein-Uhlenbeck semigroup $\{U_t\}$, any non-negative measurable $f : \mathbb R^n \to \mathbb R_+$ exhibits a uniform tail bound better than that implied by Markov's inequality and conservation of mass: For every $\alpha \geq…