Random Matrices


Introduction

Methods recently developed for the study of finitely coordinated amorphous systems can be applied to study spectra of sparse random matrices, a problem first addressed by Rodgers and Bray [Phys. Rev. B 37 , 3557-3562 (1988)]. However, the Rogers-Bray solution turned out to be extremely difficult to analyse, except in the region of large eigenvalues or large connectivities. In the general case, only approximate solutions or results of numerical diagonalizations were known until recently. Our reformulation of the problem has helped to overcome these limitations.

A second, unrelated recent effort has been devoted to analyzing the spectral problem of sample auto-covariance matrices derived from time series. In contrast to the widely studied related problem of sample covariance matrices of multivariate random data (the Wishart-Laguerre ensemble), a theoretical understanding of the spectral problem of sample auto-covariance matrices has so far been almost entirely missing, although it is clear that such understanding has signifincant potential for a broad range of applications, including time series analysis, signal processing, information theory, and finance.


Recent Talks


Recent Papers


rk  12.08.21

web counter