Related papers: Equidistribution and $\beta$ ensembles

Two-term asymptotic formulae for the probability distribution functions for the smallest eigenvalue of the Jacobi $ \beta $-Ensembles are derived for matrices of large size in the r\'egime where $ \beta > 0 $ is arbitrary and one of the…

We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N_{+}) of a random NxN matrix belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic (\beta=4)…

The Gaussian $\beta$-ensemble (G$\beta$E) is a fundamental model in random matrix theory. In this paper, we provide a comprehensive asymptotic description of the characteristic polynomial of the G$\beta$E anywhere in the bulk of the…

An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of…

In a high temperature regime where $\beta N \to 2c$, the empirical distribution of the eigenvalues of Gaussian beta ensembles, beta Laguerre ensembles and beta Jacobi ensembles converges to a limiting measure which is related to associated…

We introduce a framework to study the random entire function $\zeta_\beta$ whose zeros are given by the Sine$_\beta$ process, the bulk limit of beta ensembles. We present several equivalent characterizations, including an explicit power…

In the present context, superintegrability is a property of certain probability density functions coming from matrix models, which relates to the average over a distinguished basis of symmetric functions, typically the Jack or Macdonald…

We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. We show how the parameters of…

We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…

In this paper we consider random block matrices, which generalize the general beta ensembles, which were recently investigated by Dumitriu and Edelmann (2002, 2005). We demonstrate that the eigenvalues of these random matrices can be…

Gaussian and Chiral Beta-Ensembles, which generalise well known orthogonal (Beta=1), unitary (Beta=2), and symplectic (Beta=4) ensembles of random Hermitian matrices, are considered. Averages are shown to satisfy duality relations like…

The empirical eigenvalue distribution of the elliptic random matrix ensemble tends to the uniform measure on an ellipse in the complex plane as its dimension tends to infinity. We show this convergence on all mesoscopic scales slightly…

In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter $\theta>0$) by replacing the entries equal to one by…

For many applications, an ensemble of base classifiers is an effective solution. The tuning of its parameters(number of classes, amount of data on which each classifier is to be trained on, etc.) requires G, the generalization error of a…

We consider a set of probability measures on a finite event space $\Omega$. The mutual affinity is introduced in terms of the spectrum of the associated Gram matrix. We show that, for randomly chosen measures, the empirical eigenvalue…

We introduce constellation ensembles, in which charged particles on a line (or circle) are linked with charged particles on parallel lines (or concentric circles). We present formulas for the partition functions of these ensembles in terms…

In this paper, we give bounds on the variance of the number of points of the circular and the Gaussian $\beta$ ensemble in arcs of the unit circle or intervals of the real line. These bounds are logarithmic with respect to the renormalized…

For Y a subset of the complex plane,a beta ensemble is a sequence of probability measures on Y^n for n=1,2,3...depending on a real-valued continuous function Q and a real positive parameter beta.We consider the associated sequence of…

Consider the question: what statistical ensemble corresponds to minimal prior knowledge about a quantum system ? For the case where the system is in fact known to be in a pure state there is an obvious answer, corresponding to the unique…

The extreme eigenvalues of connectivity matrices govern the influence of the network structure on a number of network dynamical processes. A fundamental open question is whether the eigenvalues of large networks are well represented by…