Related papers: Limit Theorems on the Mesoscopic Scale for the And…
Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an optimal improvement over previous ones for…
This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated,…
We demonstrate that by considering disordered single-particle Hamiltonians (or their random matrix versions) on ultrametric spaces one can generate an interesting class of models exhibiting Anderson metal-insulator transition. We use the…
In order to characterize the fluctuation between the ergodic limit and the time-averaging estimator of a full discretization in a quantitative way, we establish a central limit theorem for the full discretization of the parabolic stochastic…
We discuss the localization behavior of localized electronic wave functions in the one- and two-dimensional tight-binding Anderson model with diagonal disorder. We find that the distributions of the local wave function amplitudes at fixed…
We study the Anderson transition on a generic model of random graphs with a tunable branching parameter $1<K\le 2$, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a…
The paper is devoted to the investigation of Esscher's transform on high dimensional Euclidean spaces in the light of its application to the central limit theorem. With this tool, we explore necessary and sufficient conditions of normal…
We study mesoscopic linear statistics for a class of determinantal point processes which interpolates between Poisson and Gaussian Unitary Ensemble statistics. These processes are obtained by modifying the spectrum of the correlation kernel…
Let $\Lambda=\{\Lambda_0,\Lambda_1,\Lambda_2,\ldots\}$ be the point process that describes the edge scaling limit of either (i) "regular" beta-ensembles with inverse temperature $\beta>0$, or (ii) the top eigenvalues of Wishart or Gaussian…
We consider random permutations on $\Sn$ with logarithmic growing cycles weights and study asymptotic behavior as the length $n$ tends to infinity. We show that the cycle count process converges to a vector of independent Poisson variables…
Fluctuations of thermodynamic quantities become non-negligible and play an important role when the system size is small. We develop finite-time thermodynamics of fluctuations in microscopic heat engines whose environmental temperature and…
For random operators it is conjectured that spectral properties of an infinite-volume operator are related to the distribution of spectral gaps of finite-volume approximations. In particular, localization and pure point spectrum in infinite…
In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…
A model in which a three-dimensional elastic medium is represented by a network of identical masses connected by springs of random strengths and allowed to vibrate only along a selected axis of the reference frame, exhibits an Anderson…
We calculate the distribution of current fluctuations in two simple exclusion models. Although these models are classical, we recover even for small systems such as a simple or a double barrier, the same distibution of current as given by…
The central limit theorem for Markov chains generated by iterated function systems consisting of orientation preserving homeomorphisms of the interval is proved. We study also ergodicity of such systems.
Mesoscopic theory for self-assembling systems near a planar confining surface is developed. Euler- Lagrange (EL) equations and the boundary conditions (BC) for the local volume fraction and the correlation function are derived from the DFT…
We consider the Anderson model with Bernoulli potential on the 3D lattice, and prove localization of eigenfunctions corresponding to eigenvalues near zero, the lower boundary of the spectrum. We follow the framework by Bourgain-Kenig and…
We report our results on the scaling limit of the eigenvalues and the corresponding eigenfunctions for the 1-d random Schr\"odinger operator with random decaying potential. The formulation of the problem is based on the paper by…
For the eigenvalues of principal submatrices of stochastically evolving Wigner matrices, we construct and study the edge scaling limit: a random decreasing sequence of continuous functions of two variables, which at every point has the…