A moment method for invariant ensembles

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doi:10.3934/era.2018.25.007

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2018, Volume 25: 60-71. Doi: 10.3934/era.2018.25.007

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A moment method for invariant ensembles

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1.
Department of Mathematics, Kagoshima University, Kagoshima, Japan
2.
Department of Mathematics, University of California, San Diego, USA

Received: April 06, 2018

Revised: September 04, 2018

Published: March 2018

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Abstract

We introduce a new moment method in Random Matrix Theory specifically tailored to the spectral analysis of invariant ensembles. Our method produces a classification of invariant ensembles which exhibit a spectral Law of Large Numbers and yields an explicit description of the limiting eigenvalue distribution when it exists. We discuss the future development and applications of this new moment method.

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Mathematics Subject Classification: Primary: 15B52.

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