相关论文: Deviation bounds for the norm of a random vector u…

Let $(S_n)_{n \geq 0}$ be a transient random walk in the domain of attraction of a stable law and let $(\xi(s))_{s \in \mathbb{Z}}$ be a stationary sequence of random variables. In a previous work, under conditions of type $D(u_n)$ and…

Given l<s<m an upper bound on the s norm is given using l norm and m norm. The result is applied in bounding odd values of zeta function, binomial sums and gamma and beta functions.

Let $B$ be a $d$-dimensional Gaussian process on $\mathbb{R}$, where the component are independents copies of a scalar Gaussian process $B_0$ on $\mathbb{R}_+$ with a given general variance function…

Distributions of strictly positive numbers are common and can be characterized by standard statistical measures such as mean, standard deviation, and skewness. We demonstrate that for these distributions the skewness $D_3$ is bounded from…

We address the problem of extrapolating the vector form factor $f_{B\pi}^+$, which is relevant to $B\to \pi\ell \nu_\ell$ decays, from the region of small to the region of large momentum transfer. As input, we use the QCD light-cone sum…

Concentration inequalities for the sample mean, like those due to Bernstein, Hoeffding, and Bentkus, are valid for any sample size but overly conservative, yielding confidence intervals that are unnecessarily wide. The central limit theorem…

Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on…

Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a nonconstant distribution, then (i) the limit distribution is…

This work introduces a new, explicit bound on the Hellinger distance between a continuous random variable and a Gaussian with matching mean and variance. As example applications, we derive a quantitative Hellinger central limit theorem and…

A well-defined variational principle for gravitational actions typically requires to cancel boundary terms produced by the variation of the bulk action with a suitable set of boundary counterterms. This can be achieved by carefully…

Let $(E, \| \cdot\|)$ be a Banach space such that, for some $q\geq 2$, the function $x\mapsto \|x\|^q$ is of $C^2$ class and its first and second Fr\'{e}chet derivatives are bounded by some constant multiples of $(q-1)$-th power of the norm…

We prove Berry-Esseen theorems, almost sure invariance principle rates and large deviations for products of independent but not identically distributed invertible matrices with some average (logarithmic) projective contraction and uniform…

Let $X$ be a symmetric, isotropic random vector in $\mathbb{R}^m$ and let $X_1...,X_n$ be independent copies of $X$. We show that under mild assumptions on $\|X\|_2$ (a suitable thin-shell bound) and on the tail-decay of the marginals…

Let $Z$ be an $n$-dimensional Gaussian vector and let $f: \mathbb R^n \to \mathbb R$ be a convex function. We show that: $$\mathbb P \left( f(Z) \leq \mathbb E f(Z) -t\sqrt{ {\rm Var} f(Z)} \right) \leq \exp(-ct^2),$$ for all $t>1$, where…

We obtain non-uniform Edgeworth expansions for several classes of weakly dependent (non-stationary) sequences of random variables, including uniformly elliptic inhomogeneous Markov chains, random and time-varying (partially) hyperbolic or…

Explicit sufficient conditions on the hypercontractivity are presented for two classes of functional stochastic partial differential equations driven by, respectively, non-degenerate and degenerate Gaussian noises. Consequently, these…

We obtain the optimal proxy variance for the sub-Gaussianity of Beta distribution, thus proving upper bounds recently conjectured by Elder (2016). We provide different proof techniques for the symmetrical (around its mean) case and the…

We prove that any random variable $X$ whose moment generating function is point-wise upper bounded by that of $ G \sim \mathcal{N}(0,1) $ must be dominated by $ G/\mathbb{E}[|G|] $ in convex order, meaning $ \mathbb{E}[f(X)] \le…

We show that the $L^1$ norm of an exponential sum of length $X$ and with coefficients equal to the Liouville or M\"{o}bius function is at least $\gg_{\varepsilon} X^{1/4 - \varepsilon}$ for any given $\varepsilon$. For the Liouville…

We consider in this paper the problem of sampling a high-dimensional probability distribution $\pi$ having a density with respect to the Lebesgue measure on $\mathbb{R}^d$, known up to a normalization constant $x \mapsto \pi(x)=…