Multicanonical sampling of rare events in random matrices

Journal Article · Wed Sep 15 00:00:00 EDT 2010 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.82.031142· OSTI ID:21464496

Saito, Nen; Iba, Yukito; Hukushima, Koji ^[1]

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1. Graduate School of Science and Cybermedia Center, Osaka University, Toyonaka, Osaka 560-0043 (Japan)

A method based on multicanonical Monte Carlo is applied to the calculation of large deviations in the largest eigenvalue of random matrices. The method is successfully tested with the Gaussian orthogonal ensemble, sparse random matrices, and matrices whose components are subject to uniform density. Specifically, the probability that all eigenvalues of a matrix are negative is estimated in these cases down to the values of {approx}10{sup -200}, a region where simple random sampling is ineffective. The method can be applied to any ensemble of matrices and used for sampling rare events characterized by any statistics.

• OSTI ID: 21464496
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 82, Issue 3; Other Information: DOI: 10.1103/PhysRevE.82.031142; (c) 2010 The American Physical Society; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENVALUES
MATRICES
MONTE CARLO METHOD
PROBABILITY
RANDOMNESS
SAMPLING
STATISTICS
CALCULATION METHODS
MATHEMATICS