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Author:   Laszlo Erdos ,  Horng-Tzer Yau
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   0.413kg
ISBN:  

9781470436483

ISBN 10:   1470436485
Pages:   226
Publication Date:   30 September 2017
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Introduction Wigner matrices and their generalizations Eigenvalue density Invariant ensembles Universality for generalized Wigner matrices Local semicircle law for universal Wigner matrices Weak local semicircle law Proof of the local semicircle law Sketch of the proof of the local semicircle law using the spectral gap Fluctuation averaging mechanism Eigenvalue location: The rigidity phenomenon Universality for matrices with Gaussian convolutions Entropy and the logarithmic Sobolev inequality (LSI) Universality of the Dyson Brownian motion Continuity of local correlation functions under the matrix OU process Universality of Wigner matrices in small energy windows: GFT Edge universality Further results and historical notes References Index

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Author Information

Laszlo Erdos, Institute of Science and Technology Austria, Klosterneuburg, Austria. Horng-Tzer Yau, Harvard University, Cambridge, MA.

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