Related papers: Normal random matrix ensemble as a growth problem

In this paper we deal with an eigenvalue problem in an interface elliptic equation. We characterize the set of principal eigenvalues as a level set of a concave and regular function. As application, we study a problem arising in population…

We consider the Gaussian ensembles of random matrices and describe the normal modes of the eigenvalue spectrum, i.e., the correlated fluctuations of eigenvalues about their most probable values. The associated normal mode spectrum is…

We consider the sum of two large Hermitian matrices $A$ and $B$ with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is…

We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…

We consider nonnormal matrix-valued dynamical systems with discrete time. For an eigenvalue of matrix, the number of times it appears as a root of the characteristic polynomial is called the algebraic multiplicity. On the other hand, the…

In this paper extremal problems for uniform hypergraphs are studied in the general setting of hereditary properties. It turns out that extremal problems about edges are particular cases of a general analyic problem about a recently…

The problem of membrane topology in the matrix model of M-theory is considered. The matrix regularization procedure, which makes a correspondence between finite-sized matrices and functions defined on a two-dimensional base space, is…

Random matrix theory has played an important role in various areas of pure mathematics, mathematical physics, and machine learning. From a practical perspective of data science, input data are usually normalized prior to processing. Thus,…

Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the…

We study the behavior of eigenvalues of matrix P_N + Q_N where P_N and Q_N are two N -by-N random orthogonal projections. We relate the joint eigenvalue distribution of this matrix to the Jacobi matrix ensemble and establish the universal…

The properties of eigenvalues of large dimensional random matrices have received considerable attention. One important achievement is the existence and identification of the limiting spectral distribution of the empirical spectral…

We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…

We study properties of eigenvalues of a matrix associated with a randomly chosen partial automorphism of a regular rooted tree. We show that asymptotically, as the numbers of levels goes to infinity, the fraction of non-zero eigenvalues…

In this paper we find spectral properties in the large $N$ limit of Dirac operators that come from random finite noncommutative geometries. In particular for a Gaussian potential the limiting eigenvalue spectrum is shown to be universal…

Motivated by a problem in learning theory, we are led to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the derivative of random polynomials (generated by picking their roots…

We study the convergence properties of a pair of learning algorithms (learning with and without memory). This leads us to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the…

The problem of the onset and growth of solid tumour in homogeneous tissue is regarded using an approach based on local interaction between the tumoral and the sane tissue cells. The characteristic sizes and growth rates of spherical…

In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…

We carry out a numerical study of fluctuations in the spectrum of regular graphs. Our experiments indicate that the level spacing distribution of a generic k-regular graph approaches that of the Gaussian Orthogonal Ensemble of random matrix…

In contemporary applied and computational mathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent random matrices. This quantity is controlled by the norm of the expected square of the…