Related papers: A Bernstein Inequality For Spatial Lattice Process…
This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav…
We show that the mixing times of random walks on compact groups can be used to obtain concentration inequalities for the respective Haar measures. As an application, we derive a concentration inequality for the empirical distribution of…
Semiparametric mixture models are parametric models with latent variables. They are defined kernel, $p_\theta(x | z)$, where z is the unknown latent variable, and $\theta$ is the parameter of interest. We assume that the latent variables…
The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes, especially stochastic integrals and differential equations. In this paper, general central limit theorems and functional…
Using Stein's method techniques, we develop a framework which allows one to bound the error terms arising from approximation by the Laplace distribution and apply it to the study of random sums of mean zero random variables. As a corollary,…
We give a method to obtain, from Voiculescu's inequality, norm estimates for sums of free variables with amalgamation in general fully symmetric spaces. We use these estimates to interpolate the Burkholder inequalities for non commutative…
Computing the agreement between two continuous sequences is of great interest in statistics when comparing two instruments or one instrument with a gold standard. The probability of agreement (PA) quantifies the similarity between two…
We present new bounds for the Berezin number inequalities which improve on the existing bounds. We also obtain bounds for the Berezin norm of operators as well as the sum of two operators.
We consider weak solutions of the inhomogeneous non-cutoff Boltzmann equation in a bounded domain with any of the usual physical boundary conditions: in-flow, bounce-back, specular-reflection and diffuse-reflection. When the mass, energy…
We give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions of independent random variables. Since weighted lattice polynomial functions include…
We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and…
We propose a method to measure the Witten index using lattice simulation. A requirement for the lattice model is that it has at least one exact supersymmetry at finite lattice spacing. We prove the validity of the method in case of the…
Random Ising systems on a general hierarchical lattice with both, random fields and random bonds, are considered. Rigorous inequalities between eigenvalues of the Jacobian renormalization matrix at the pure fixed point are obtained. These…
A method that uses order statistics to construct multivariate distributions with fixed marginals and which utilizes a representation of the Bernstein copula in terms of a finite mixture distribution is proposed. Expectation-maximization…
This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in…
We present a new Schwarz Lemma for bounded domains with Bergman metrics. The key ingredient of our proof is the Cauchy-Schwarz inequality from probability theory.
A hybrid lattice Boltzmann method (LBM) for binary mixtures based on the free-energy approach is proposed. Non-ideal terms of the pressure tensor are included as a body force in the LBM kinetic equations, used to simulate the continuity and…
We say that one point process on the line $\mathbb{R}$ mimics another at a bandwidth $B$ if for each $n \ge 1$ the two point processes have $n$-level correlation functions that agree when integrated against all bandlimited test functions on…
We extend the classical Bernstein technique to the setting of integro-differential operators. As a consequence, we provide first and one-sided second derivative estimates for solutions to fractional equations, including some convex fully…
We outline a general procedure on how to apply random positive linear operators in nonparametric estimation. As a consequence, we give explicit confidence bands and intervals for a distribution function $F$ concentrated on $[0,1]$ by means…