Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices - Condensed Matter > Statistical MechanicsReportar como inadecuado




Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices - Condensed Matter > Statistical Mechanics - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We present a simple Coulomb gas method to calculate analytically theprobability of rare events where the maximum eigenvalue of a random matrix ismuch larger than its typical value. The large deviation function thatcharacterizes this probability is computed explicitly for Wishart and Gaussianensembles. The method is quite general and applies to other related problems,e.g. the joint large deviation function for large fluctuations of topeigenvalues. Our results are relevant to widely employed data compressiontechniques, namely the principal components analysis. Analytical predictionsare verified by extensive numerical simulations.



Autor: Satya N. Majumdar, Massimo Vergassola

Fuente: https://arxiv.org/







Documentos relacionados