Work

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

Year: 2009

Type: article

Abstract: We present a 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 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.

Source: Physical Review Letters

DOI: 10.1103/physrevlett.102.060601

Authors: Satya N. Majumdar, Massimo Vergassola

Institutions: Université Paris-Sud, Centre National de la Recherche Scientifique, Laboratoire de Physique Théorique et Modèles Statistiques, Institut Pasteur, Department of Genomes & Genetics

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2145204138

FWCI: 8.472

Cites: 30

Cited by: 152

Related to: 10