4 papers
Lecture notes on random matrix theory: the results, the applications, and the analytical tools
Joseph W. Baron
Random matrix theory has established itself as a theoretical cornerstone of the mathematical sciences over the past century. It has undeniable utility in areas of research as diver…
Local density of states distribution and multifractal eigenvectors of weighted random networks via the cavity approach
Joseph W. Baron, Tim Rogers
We study the local density of states (LDoS) distribution of a general class of weighted Erdős-Rényi graphs. Using the cavity method, we obtain a good approximation to the full LDoS…
Eigenvalue spectral tails and localization properties of asymmetric networks
Pietro Valigi, Joseph W. Baron, Izaak Neri +2
In contrast to the neatly bounded spectra of densely populated large random matrices, sparse random matrices often exhibit unbounded eigenvalue tails on the real and imaginary axis…
Classes of non-Gaussian random matrices: long-range eigenvalue correlations and non-ergodic extended eigenvectors
Joseph W. Baron
The remarkable universality of the eigenvalue correlation functions is perhaps one of the most salient findings in random matrix theory. Particularly for short-range separations of…