Related papers: Non-central limit theorems for random fields subor…
We construct a family of measures for random fields based on the iterated subdivision of simple geometric shapes (triangles, squares, tetrahedrons) into a finite number of similar shapes. The intent is to construct continuum limits of scale…
We derive sharp upper and lower bounds for the pointwise concentration function of the maximum statistic of $d$ identically distributed real-valued random variables. Our first main result places no restrictions either on the common marginal…
The conditions for the existence of the effective action in statistical field theory, the Legendre transform of the cumulant generating function, in presence of non-linear local constraints are discussed. This problem is of importance for…
Non-linear d-dimensional vector $\sigma$-models are studied in the large N-limit. It is found that a two-point correlation function obeys a standard Schrodinger equation for a free quantum particle moving in the $\delta$-function quantum…
We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply…
The purpose of this note is to recall one remarkable theorem of Khinchin about the special role of the Gaussian distribution. This theorem allows us to give a new interpretation of the Lindeberg condition: it guarantees the uniform…
We establish a central limit theorem for the central values of Dirichlet $L$-functions with respect to a weighted measure on the set of primitive characters modulo $q$ as $q \rightarrow \infty$. Under the Generalized Riemann Hypothesis…
We study the distribution modulo $1$ of the values taken on the integers of $r$ linear forms in $d$ variables with random coefficients. We obtain quenched and annealed central limit theorems for the number of simultaneous hits into…
This paper presents likelihood-based inference methods for the family of univariate gamma-normal distributions GN({\alpha}, r, {\mu}, {\sigma}^2 ) that result from summing independent gamma({\alpha}, r) and N({\mu}, {\sigma}^2 ) random…
It has been well known for a long time that the height function of random lozenge tilings of large domains follow a law of large number and possible limits called dimer limit shapes are well understood. For the next order, it is expected…
We provide asymptotic results for the distribution of weighted nonlinear functionals of Gaussian field with long-range dependence. We also show that integral functionals and the corresponding additive functionals have same distributions…
We consider the determinantal point processes associated with the spectral projectors of a Schr\"odinger operator on $\mathbb{R}$, with a smooth confining potential. In the semiclassical limit, where the number of particles tends to…
Berry-Esseen bounds for non-linear functionals of infinite Rademacher sequences are derived by means of the Malliavin-Stein method. Moreover, multivariate extensions for vectors of Rademacher functionals are shown. The results establish a…
The paper considers the distribution of a general linear combination of central and non-central chi-square random variables by exploring the branch cut regions that appear in the standard Laplace inversion process. Due to the original…
We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting…
We study the free central limit theorem for not necessarily identically distributed free random variables where the limiting distribution is the semicircle distribution. Starting from an estimate for the Kolmogorov distance between the…
In this note, we establish that the stationary distribution of a possibly non-equilibrium Langevin diffusion converges, as the damping parameter goes to infinity (or equivalently in the Smoluchowski-Kramers vanishing mass limit), toward a…
We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to $\infty$. The random fields considered include costs…
Weak convergence of maxima of dependent sequences of identically distributed continuous random variables is studied under normalizing sequences arising as subsequences of the normalizing sequences from an associated iid sequence. This…
Quantitative limit theorems for non-linear functionals on the Wiener space are considered. Given the possibly infinite sequence of kernels of the chaos decomposition of such a functional, an estimate for different probability distances…