Non-Hermitian Random Matrices
Ginibre ensembles, circular laws, and pseudospectra.
Non-Hermitian Random Matrices. Ginibre ensembles, circular laws, and pseudospectra.
Foundations and canonical references
The standard treatments of non-hermitian random matrices approach the subject from complementary angles. Anderson, An Introduction to Random Matrices (2010) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.
Recent technical contributions
A handful of recent papers carry the methodological frontier of non-hermitian random matrices forward. On the rightmost eigenvalue of non-Hermitian random matrices (Cipolloni, 2023) is a primary reference for this area and develops new techniques or results that downstream work builds on.
Open methodological questions for non-hermitian random matrices include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
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- textbook · supporting · 2010An Introduction to Random Matricesanderson-2010, guionnet-2010, zeitouni-2010
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