Related papers: Limit Theorems on the Mesoscopic Scale for the And…
We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…
In this paper, we explain the dependance of the fluctuations of the largest eigenvalues of a Deformed Wigner model with respect to the eigenvectors of the perturbation matrix. We exhibit quite general situations that will give rise to…
We consider the adjacency matrix $A$ of a large random graph and study fluctuations of the function $f_n(z,u)=\frac{1}{n}\sum_{k=1}^n\exp\{-uG_{kk}(z)\}$ with $G(z)=(z-iA)^{-1}$. We prove that the moments of fluctuations normalized by…
We establish a central limit theorem for the eigenvalue counting function of a matrix of real Gaussian random variables.
We study the statistics of Dirichlet eigenvalues of the random Schr\"odinger operator $-\epsilon^{-2}\Delta^{(\text{d})}+\xi^{(\epsilon)}(x)$, with $\Delta^{(\text{d})}$ the discrete Laplacian on $\mathbb Z^d$ and $\xi^{(\epsilon)}(x)$…
There is a widespread recent interest in using ideas from statistical physics to model certain types of problems in economics and finance. The main idea is to derive the macroscopic behavior of the market from the random local interactions…
We study the eigenvalue statistics for the hieracharchial Anderson model of Molchanov. We prove Poisson fluctuations at arbitrary disorder, when the the model has spectral dimension d<1. The proof is based on Minami's technique and we give…
We consider the Anderson model on a strip. Assuming that potentials have bounded density with considerable tails we get a lower bound for the fluctuations of the logarithm of the Green's function in a finite box. This implies an effective…
We study the linear eigenvalue statistics of large random graphs in the regimes when the mean number of edges for each vertex tends to infinity. We prove that for a rather wide class of test functions the fluctuations of linear eigenvalue…
We prove central limit theorem for linear eigenvalue statistics of orthogonally invariant ensembles of random matrices with one interval limiting spectrum. We consider ensembles with real analytic potentials and test functions with two…
Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…
We consider eigenvalues of generalized Wishart processes as well as particle systems, of which the empirical measures converge to deterministic measures as the dimension goes to infinity. In this paper, we obtain central limit theorems to…
We prove a Central Limit Theorem for the linear statistics of two-dimensional Coulomb gases, with arbitrary inverse temperature and general confining potential, at the macroscopic and mesoscopic scales and possibly near the boundary of the…
We study the statistical properties of the entropic optimal (self) transport problem for smooth probability measures. We provide an accurate description of the limit distribution for entropic (self-)potentials and plans as the…
Using the Anderson model for disordered systems the fluctuations in electron spectra near the metal--insulator transition were numerically calculated for lattices of sizes up to 28 x 28 x 28 sites. The results show a finite--size scaling of…
We prove localization and probabilistic bounds on the minimum level spacing for the Anderson tight-binding model on the lattice in any dimension, with single-site potential having a discrete distribution taking N values, with N large.
We discuss the role of rare fluctuation effects in quantum condensed matter systems. In particular, we present recent numerical results of the effect of resonant states in Anderson's original model of electron localization. We find that…
Fluctuations of the order parameters of the Gardner model for any $\alpha<\alpha_c$ are studied. It is proved that they converge in distribution to a family of jointly Gaussian random variables.
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 study the limiting behavior of smooth linear statistics of the spectrum of random permutation matrices in the mesoscopic regime, when the permutation follows one of the Ewens measures on the symmetric group. If we apply a smooth enough…