Related papers: Random commuting matrices

The statistical properties of trajectories of eigenvalues of Gaussian complex matrices whose Hermitian condition is progressively broken are investigated. It is shown how the ordering on the real axis of the real eigenvalues is reflected in…

We consider $N\times N$ random matrices of the form $H=W+V$ where $W$ is a real symmetric or complex Hermitian Wigner matrix and $V$ is a random or deterministic, real, diagonal matrix whose entries are independent of $W$. We assume…

Let $D$ denote the distance matrix for an $n+1$ point metric space $(X,d)$. In the case that $X$ is an unweighted metric tree, the sum of the entries in $D^{-1}$ is always equal to $2/n$. Such trees can be considered as affinely independent…

We develop a theory which describes the behaviour of eigenvalues of a class of one-dimensional random non-Hermitian operators introduced recently by Hatano and Nelson. Under general assumptions on random parameters we prove that the…

We construct a random matrix model for the bijection \Psi between clas- sical and free infinitely divisible distributions: for every d\geq1, we associate in a quite natural way to each *-infinitely divisible distribution \mu a distribution…

We characterize asymptotic collective behaviour of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are…

Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous…

Evidences have suggested that counting representations are sometimes tractable even when the corresponding classification problem is almost impossible, or "wild" in a precise sense. Such counting problems are directly related to matrix…

We describe Generalized Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We will calculate a Laplace transform of such a density for finite…

For fixed $m>1$, we consider $m$ independent $n \times n$ non-Hermitian random matrices $X_1, ..., X_m$ with i.i.d. centered entries with a finite $(2+\eta)$-th moment, $ \eta>0.$ As $n$ tends to infinity, we show that the empirical…

We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first…

We consider the density of states of structured Hermitian random matrices with a variance profile. As the dimension tends to infinity the associated eigenvalue density can develop a singularity at the origin. The severity of this…

A recursive method is derived to calculate all eigenvalue correlation functions of a random hermitian matrix in the large size limit, and after smoothing of the short scale oscillations. The property that the two-point function is…

Consider a Hermitian matrix model under an external potential with spiked external source. When the external source is of rank one, we compute the limiting distribution of the largest eigenvalue for general, regular, analytic potential for…

Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability density function for the corresponding spacings between…

Let $R$ be a finite ring. The commuting probability of $R$, denoted by $\Pr(R)$, is the probability that any two randomly chosen elements of $R$ commute. $R$ is called an $n$-centralizer ring if it has $n$ distinct centralizers. In this…

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…

Some randomized algorithms, used to obtain a random $n^2 \times n^2$ Sudoku matrix, where $n$ is a natural number, is reviewed in this study. Below is described the set $\Pi_n$ of all $(2n) \times n$ matrices, consisting of elements of the…

We show that the average characteristic polynomial P_n(z) = E [\det(zI-M)] of the random Hermitian matrix ensemble Z_n^{-1} \exp(-Tr(V(M)-AM))dM is characterized by multiple orthogonality conditions that depend on the eigenvalues of the…

We study the eigenvalue trajectories of a time dependent matrix $ G_t = H+i t vv^*$ for $t \geq 0$, where $H$ is an $N \times N$ Hermitian random matrix and $v$ is a unit vector. In particular, we establish that with high probability, an…