Chapter

Universality of generalized Wigner matrices

Horng-Tzer Yau

in Quantum Theory from Small to Large Scales

Published in print May 2012 | ISBN: 9780199652495
Published online September 2012 | e-ISBN: 9780191741203 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199652495.003.0014

Series: Lecture Notes of the Les Houches Summer School

Universality of generalized Wigner matrices

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This chapter reviews recent progress on the universality of eigenvalue distributions of generalized Wigner matrices in the bulk and at the edges. It discusses first the local semicircle law, which underlies many of the results. Universality for Gaussian divisible ensembles is then established via the local relaxation flow. Finally, the results are extended to general ensembles by Green's function comparison theorem.

Keywords: random matrices; Local semicircle law; Tracy-Widom distribution; Dyson Brownian motion

Chapter.  7572 words. 

Subjects: Atomic, Molecular, and Optical Physics

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