Related papers: Percolation in a Class of Band Structured Random M…

Eigenvalues of Wigner matrices has been a major topic of investigation. A particularly important subclass of such random matrices is formed by the adjacency matrix of an Erd\H{o}s-R\'{e}nyi graph $\mathcal{G}_{n,p}$ equipped with i.i.d.…

We give a physical description in terms of percolation theory of the phase transition that occurs when the disorder increases in the random antiferromagnetic spin-1 chain between a gapless phase with topological order and a random singlet…

A sum of a large-dimensional random matrix polynomial and a fixed low-rank matrix polynomial is considered. The main assumption is that the resolvent of the random polynomial converges to some deterministic limit. A formula for the limit of…

We prove a concentration phenomenon on the empirical eigenvalue distribution (EED) of the principal submatrix in a random hermitian matrix whose distribution is invariant under unitary conjugacy; for example, this class includes GUE…

We consider random hermitian matrices made of complex blocks. The symmetries of these matrices force them to have pairs of opposite real eigenvalues, so that the average density of eigenvalues must vanish at the origin. These densities are…

Let a random geometric graph be defined in the supercritical regime for the existence of a unique infinite connected component in Euclidean space. Consider the first-passage percolation model with independent and identically distributed…

An exchangeable random matrix is a random matrix with distribution invariant under any permutation of the entries. For such random matrices, we show, as the dimension tends to infinity, that the empirical spectral distribution tends to the…

We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…

We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution…

In random-matrix ensembles that interpolate between the three basic ensembles (orthogonal, unitary, and symplectic), there exist correlations between elements of the same eigenvector and between different eigenvectors. We study such…

The statistics of equally weighted random paths (ideal polymer) is studied in $2$ and $3$ dimensional percolating clusters. This is equivalent to diffusion in the presence of a trapping environment. The number of $N$ step walks follows a…

We consider level crossing in a matrix family $H=H_0+\lambda V$ where $H_0$ is a fixed $N\times N$ matrix and $V$ belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing…

Three recently suggested random matrix ensembles (RME) are linked together by an exact mapping and plausible conjections. Since it is known that in one of these ensembles the eigenvector statistics is multifractal, we argue that all three…

Motivated by an investigation of ground state properties of randomly charged polymers, we discuss the size distribution of the largest Q-segments (segments with total charge Q) in such N-mers. Upon mapping the charge sequence to…

We study oriented percolation on random causal triangulations, those are random planar graphs obtained roughly speaking by adding horizontal connections between vertices of an infinite tree. When the underlying tree is a geometric…

In this article we consider the spectrum of a Laplacian matrix, also known as the Markov matrix, under the independence assumption. We assume that the entries have a variance profile. Motivated by recent works on generalized Wigner matrices…

Let $A$ and $B$ be independent, central Wishart matrices in $p$ variables with common covariance and having $m$ and $n$ degrees of freedom, respectively. The distribution of the largest eigenvalue of $(A+B)^{-1}B$ has numerous applications…

We study the asymptotic distribution of level crossings for random matrix pencils A_n+\lambda B_n in several ensembles, including complex and real i.i.d. matrices and Gaussian/Hermitian settings. We derive a representation of the normalized…

A theory is presented (and supported by numerical simulations) for phase-coherent reflection of light by a disordered medium which either absorbs or amplifies radiation. The distribution of reflection eigenvalues is shown to be the Laguerre…

Using the standard concepts of free random variables, we show that for a large class of nonhermitean random matrix models, the support of the eigenvalue distribution follows from their hermitean analogs using a conformal transformation. We…