Universality of random matrices and local relaxation flow | Zendy

László Erdős | Zendy; Benjamin Schlein | Zendy; HorngTzer Yau | Zendy

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Universality of random matrices and local relaxation flow

Author(s) -

László Erdős,

Benjamin Schlein,

HorngTzer Yau

Publication year - 2010

Publication title -

inventiones mathematicae

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 5.536

H-Index - 125

eISSN - 1432-1297

pISSN - 0020-9910

DOI - 10.1007/s00222-010-0302-7

Subject(s) - mathematics , random matrix , eigenvalues and eigenvectors , brownian motion , universality (dynamical systems) , hermitian matrix , gaussian , mathematical analysis , quaternion , mathematical physics , statistical physics , combinatorics , pure mathematics , quantum mechanics , geometry , physics , statistics

We consider $N\times N$ symmetric random matrices where the probabilitydistribution for each matrix element is given by a measure $\nu$ with asubexponential decay. We prove that the eigenvalue spacing statistics in thebulk of the spectrum for these matrices and for GOE are the same in the limit$N \to \infty$. Our approach is based on the study of the Dyson Brownian motionvia a related new dynamics, the local relaxation flow.

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