Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices

Simple item page
dc.creatorMajumdar, Satya N.
dc.creatorVergassola, Massimo
dc.date2008-11-14
dc.date.accessioned2026-07-07T12:46:59Z
dc.date.available2026-07-07T12:46:59Z
dc.descriptionWe present a simple Coulomb gas method to calculate analytically the probability of rare events where the maximum eigenvalue of a random matrix is much larger than its typical value. The large deviation function that characterizes this probability is computed explicitly for Wishart and Gaussian ensembles. The method is quite general and applies to other related problems, e.g. the joint large deviation function for large fluctuations of top eigenvalues. Our results are relevant to widely employed data compression techniques, namely the principal components analysis. Analytical predictions are verified by extensive numerical simulations.
dc.description4 pages, 3 .eps figures included
dc.identifierhttps://arxiv.org/abs/0811.2290
dc.identifierhttp://arxiv.org/abs/0811.2290
dc.identifierPhys.Rev.Lett.102:060601,2009
dc.identifierdoi:10.1103/PhysRevLett.102.060601
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221569
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.titleLarge Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices
dc.typetext

Files

Collections

arXiv