Related papers: Berry-Esseen bounds in local limit theorems
We consider the gradient field model in $\left[ -N,N\right] ^{2}\cap \mathbb{Z}^{2}$ with a uniformly convex interaction potential. Naddaf-Spencer \cite{NS} and Miller \cite{Mi} proved that the macroscopic averages of linear statistics of…
Leptons, quarks and gauge bosons are assumed to be described by local field theory. Stringent bounds on nonlocal scale can be derived from the high- presision LEP measurements. We find a bound on nonlocal scale $\Lambda_{nl} > 1020\: Gev$,…
In this paper, we obtain uniform bounds for a number of expressions that involve derivatives and integrals of modified Bessel functions. These uniform bounds are motivated by the need to bound such expressions in the study of variance-gamma…
We discuss localized ground states of the periodic Gross-Pitaevskii equation in the framework of a quantum linear Schr\"odinger equation with effective potential determined in self-consistent manner. We show that depending on the…
The class of problems treated here are elliptic partial differential equations with a homogeneous boundary condition and a non-linear perturbation obtained by composition with a fixed smooth function. The existence of solutions is obtained…
We obtain a Bourgain-Br\'ezis-Mironescu formula on the limit behaviour of a modified fractional Sobolev seminorm when $s\nearrow 1$, which is valid in arbitrary bounded domains. In the case of extension domains, we recover the classical…
We give a sufficient condition for the local limit theorem. To construct it, we employ infinite times of convolutions of probability density functions.
A Berry--Ess\'{e}en theorem for linear combinations of iterates of an inner function is obtained. Our proof, which is based an elementary transfer argument and classical results in martingale theory, also leads to a simple proof of Nicolau…
Limits of densities belonging to an exponential family appear in many applications, {e.g.} Gibbs models in Statistical Physics, relaxed combinatorial optimization, coding theory, critical likelihood computations, Bayes priors with singular…
Variation of empirical Fr\'echet means on a metric space with curvature bounded above is encoded via random fields indexed by unit tangent vectors. A central limit theorem shows these random tangent fields converge to a Gaussian such field…
In this paper, we study the boundedness of a class of fractional integrals and derivatives associated with Laguerre polynomial expansions on Laguerre Lipschitz spaces. The consideration of such operators is motivated by the study of…
We prove local-in-time existence and uniqueness of an inviscid Boussinesq-type system. We assume the density equation contains nonzero diffusion and that our initial vorticity and density belong to a space of borderline Besov type.
his study presents a novel technique to estimate the computational complexity of sequential decoding using the Berry-Esseen theorem. Unlike the theoretical bounds determined by the conventional central limit theorem argument, which often…
We state and prove estimates for the local boundedness of subsolutions of non-local, possibly degenerate, parabolic integro-differential equations of the form \begin{equation*} \partial_tu(x,t)+\mbox{P.V.}\int\limits_{\mathbb R^n}K(x,y,t)…
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…
We consider functionals which are weighted averages of the avoidance function of a Poisson process. Using the approach to Stein's method based on Malliavin calculus for Poisson functionals we provide explicit bounds for the Wasserstein…
We prove a range of $L^p$ bounds for singular Brascamp-Lieb forms with cubical structure. We pass through sparse and local bounds, the latter proved by an iteration of Fourier expansion, telescoping, and the Cauchy-Schwarz inequality. We…
This work is the continuation of the recent paper \cite{D2} devoted to the density-dependent incompressible Euler equations. Here we concentrate on the well-posedness issue in Besov spaces of type $B^s_{\infty,r}$ embedded in the set of…
The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic dynamics developed by the first author \textit{et al}. to establish quenched versions of the large deviation…
We propose to use quantized Berry phases as local order parameters of gapped quantum liquids, which are invariant under some anti-unitary operation. After presenting a general prescription, the scheme is applied for Heisenberg models with…