Related papers: Incremental universality of Wigner random matrices
It is well-known that distances in random iid matrices are highly concentrated around their mean. In this note we extend this concentration phenomenon to Wigner matrices. Exponential bounds for the lower tail are also included.
We exhibit a one to one correspondence between some universal probabilistic properties of the ordering coordinate of one-dimensional Ising-like models and a class of continuous time random walks. This correspondence provides an new…
The paper contains two main parts: in the first part, we analyze the general case of $p\geq 2$ matrices coupled in a chain subject to Cauchy interaction. Similarly to the Itzykson-Zuber interaction model, the eigenvalues of the Cauchy chain…
We introduce random matrix ensembles that correspond to the infinite families of irreducible Riemannian symmetric spaces of type I. In particular, we recover the Circular Orthogonal and Symplectic Ensembles of Dyson, and find other families…
Many results that are difficult can be found more easily by using a generalization in the complex plane of Einstein's addition law of parallel velocities. Such a generalization is a natural way to add quantities that are limited to bounded…
Universal dimensionless quantities, such as Binder ratios and wrapping probabilities, play an important role in the study of critical phenomena. We study the finite-size scaling behavior of the wrapping probability for the Potts model in…
We calculate analytically the probability of large deviations from its mean of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we show that the…
We study S-matrix correlations for random matrix ensembles with a Hamiltonian which is the sum of a given deterministic part and of a random matrix with a Gaussian probability distribution. Using Efetov's supersymmetry formalism, we show…
The class of norm-dependent Random Matrix Ensembles is studied in the presence of an external field. The probability density in those ensembles depends on the trace of the squared random matrices, but is otherwise arbitrary. An exact…
The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for…
We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
In these notes we review recent progress (and, in Section \ref{sec:ados}, we announce a new result) concerning the statistical properties of the spectrum of Wigner random matrices.
We study ensembles of sparse random block matrices generated from the adjacency matrix of a Erd\"os-Renyi random graph with $N$ vertices of average degree $Z$, inserting a real symmetric $d \times d$ random block at each non-vanishing…
We prove the edge universality of the beta ensembles for any $\beta\ge 1$, provided that the limiting spectrum is supported on a single interval, and the external potential is $\mathscr{C}^4$ and regular. We also prove that the edge…
We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, $W\sim N$. All previous results concerning…
We show that the distribution of the time delay for one-dimensional random potentials is universal in the high energy or weak disorder limit. Our analytical results are in excellent agreement with extensive numerical simulations carried out…
A general formulation of translationally invariant, parametrically correlated random matrix ensembles, is used to classify universality in correlation functions. Surprisingly, the range of possible physical systems is bounded, and can be…
Non-Hermitian random matrices enjoy non-trivial correlations in the statistics of their eigenvectors. We study the overlap among left and right eigenvectors in Ginibre ensembles with quaternion valued Gaussian matrix elements. This concept…
Universality of local eigenvalue statistics is one of the most striking phenomena of Random Matrix Theory, that also accounts for a lot of the attention that the field has attracted over the past 15 years. In this paper we focus on the…