2014/02/10 by Mireille Capitaine, Sandrine Péché, Capitaine, M. +1 · 1 citation
Mathematics · #Random Matrices and Applications #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics
paper · doi:10.48550/arxiv.1402.2262
We consider a full rank deformation of the GUE WN+AN where AN is a full rank Hermitian matrix of size N and WN is a GUE. The empirical eigenvalue distribution μAN of AN converges to a probability distribution ν. We identify all the possible limiting eigenvalue statistics at the edges of the spectrum, including outliers, edges and merging points of connected components of the limiting spectrum. The results are stated in terms of a deterministic equivalent of the empirical eigenvalue distribution of WN+AN, namely the free convolution of the semi-circle distribution and the empirical eigenvalues distribution of AN.