Related papers: A sufficient condition for local limit theorem

We consider the directed polymer model in the weak disorder phase under the assumption that the partition function is $L^p$-bounded for some $p>1+\frac{2}d$. We prove that the point-to-point partition function can be approximated by two…

This note gives a first sufficient condition that insures a non-negative, locally bounded, local solution to a logarithmically singular parabolic equation is continuous at a vanishing point and an estimate of the modulus of continuity is…

Consider a stochastic process $\mathfrak{X}$, regenerative at a state $x$ which is instantaneous and regular. Let $L$ be a regenerative local time for $\mathfrak{X}$ at $x$. Suppose furthermore that $\mathfrak{X}$ can be approximated by…

We prove a quantitative local limit theorem for the number of descents in a random permutation. Our proof uses a conditioning argument and is based on bounding the characteristic function $\phi(t)$ of the number of descents. We also…

We prove a local limit theorem for nearest neighbours random walks in stationary random environment of conductances on Z without using any of both classic assumptions of uniform ellipticity and independence on the conductances. Besides the…

In this paper we continue our study of local rigidity for maps of CR submanifolds of the complex space. We provide a linear sufficient condition for local rigidity of finitely nondegenerate maps between minimal CR manifolds. Furthermore, we…

We consider several examples of probabilistic existence proofs using compressibility arguments, including some results that involve Lov\'asz local lemma.

In this paper, we propose a new interpretation of local limit theorems for univariate and multivariate distributions on lattices. We show that - given a local limit theorem in the standard sense - the distributions are approximated well by…

This paper describes the quality of convergence to an infinitely divisible law relative to free multiplicative convolution. We show that convergence in distribution for products of identically distributed and infinitesimal free random…

We define the local empirical process, based on $n$ i.i.d. random vectors in dimension $d$, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical…

Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems -- yielding a Gaussian density multiplied by a highly oscillatory…

We give the first mathematically rigorous justification of the Local Density Approximation in Density Functional Theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density…

In this paper we present a new proof of the sufficiency theorem for strong local minimizers concerning $C^1$-extremals at which the second variation is strictly positive. The results are presented in the quasiconvex setting, in accordance…

We prove a local limit theorem for the Euclidian algorithms ; standard, centred and odd, with any cost function of moderate growth.

We prove a Fourier restriction estimate under the assumption that certain convolution power of the measure admits an $r$-integrable density.

We prove the Local Limit Theorems for bounded additive functionals of uniformly elliptic inhomogeneous Markov arrays. As an application we obtain the precise asymptotics in the large deviation regime for bounded additive functionals of…

In this paper we present a new correlation inequality and use it for proving an Almost Sure Local Limit Theorem for the so-called Dickman distribution. Several related results are also proved

In this paper we prove the necessity of the main sufficient condition of Meinardus for sub exponential rate of growth of the number of structures, having multiplicative generating functions of a general form and establish a new necessary…

In this paper we study the convergence in distribution and the local limit theorem for the partial sums of linear random fields with i.i.d. innovations that have infinite second moment and belong to the domain of attraction of a stable law…

We prove several limit theorems for a simple class of partially hyperbolic fast-slow systems. We start with some well know results on averaging, then we give a substantial refinement of known large (and moderate) deviation results and…