作者：Baik, Jinho; Bothner, Thomas
作者单位：University of Michigan System; University of Michigan; University of London; King's College London
摘要：The real Ginibre ensemble consists of n x n real matrices X whose entries are i.i.d. standard normal random variables. In sharp contrast to the complex and quaternion Ginibre ensemble, real eigenvalues in the real Ginibre ensemble attain positive likelihood. In turn, the spectral radius R-n = max(1 <= j <= n) vertical bar z(j)(X)vertical bar of the eigenvalues z(j)(X) is an element of C of a real Ginibre matrix X follows a different limiting law (as n -> infinity) for z(j) (X) is an element of...
作者：Bardenet, Remi; Hardy, Adrien
作者单位：Universite de Lille; Centrale Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Inria
摘要：We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical N-1/2, where N is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures involving determinantal point processes associated with multivariate orthogonal polynomials, and we obtain root mean square errors that decrease as N-(1+1/ d)/2, where d is the dimension of the ambient space. First, we prove a central limit theorem (CLT) for the lin...
