{"date_published":"2011-07-01T00:00:00Z","issue":"1","date_created":"2018-12-11T11:59:29Z","day":"01","publication_status":"published","author":[{"full_name":"László Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"first_name":"Benjamin","full_name":"Schlein, Benjamin","last_name":"Schlein"},{"last_name":"Yau","first_name":"Horng","full_name":"Yau, Horng-Tzer"}],"doi":"10.1007/s00222-010-0302-7","intvolume":"       185","publisher":"Springer","title":"Universality of random matrices and local relaxation flow","quality_controlled":0,"extern":1,"_id":"2764","abstract":[{"text":"Consider the Dyson Brownian motion with parameter β, where β=1,2,4 corresponds to the eigenvalue flows for the eigenvalues of symmetric, hermitian and quaternion self-dual ensembles. For any β≥1, we prove that the relaxation time to local equilibrium for the Dyson Brownian motion is bounded above by N -ζ for some ζ&gt; 0. The proof is based on an estimate of the entropy flow of the Dyson Brownian motion w. r. t. a &quot;pseudo equilibrium measure&quot;. As an application of this estimate, we prove that the eigenvalue spacing statistics in the bulk of the spectrum for N×N symmetric Wigner ensemble is the same as that of the Gaussian Orthogonal Ensemble (GOE) in the limit N→∞. The assumptions on the probability distribution of the matrix elements of the Wigner ensemble are a subexponential decay and some minor restriction on the support.","lang":"eng"}],"date_updated":"2021-01-12T06:59:32Z","publist_id":"4126","type":"journal_article","status":"public","month":"07","year":"2011","publication":"Inventiones Mathematicae","volume":185,"citation":{"ista":"Erdös L, Schlein B, Yau H. 2011. Universality of random matrices and local relaxation flow. Inventiones Mathematicae. 185(1), 75–119.","ama":"Erdös L, Schlein B, Yau H. Universality of random matrices and local relaxation flow. <i>Inventiones Mathematicae</i>. 2011;185(1):75-119. doi:<a href=\"https://doi.org/10.1007/s00222-010-0302-7\">10.1007/s00222-010-0302-7</a>","ieee":"L. Erdös, B. Schlein, and H. Yau, “Universality of random matrices and local relaxation flow,” <i>Inventiones Mathematicae</i>, vol. 185, no. 1. Springer, pp. 75–119, 2011.","mla":"Erdös, László, et al. “Universality of Random Matrices and Local Relaxation Flow.” <i>Inventiones Mathematicae</i>, vol. 185, no. 1, Springer, 2011, pp. 75–119, doi:<a href=\"https://doi.org/10.1007/s00222-010-0302-7\">10.1007/s00222-010-0302-7</a>.","short":"L. Erdös, B. Schlein, H. Yau, Inventiones Mathematicae 185 (2011) 75–119.","chicago":"Erdös, László, Benjamin Schlein, and Horng Yau. “Universality of Random Matrices and Local Relaxation Flow.” <i>Inventiones Mathematicae</i>. Springer, 2011. <a href=\"https://doi.org/10.1007/s00222-010-0302-7\">https://doi.org/10.1007/s00222-010-0302-7</a>.","apa":"Erdös, L., Schlein, B., &#38; Yau, H. (2011). Universality of random matrices and local relaxation flow. <i>Inventiones Mathematicae</i>. Springer. <a href=\"https://doi.org/10.1007/s00222-010-0302-7\">https://doi.org/10.1007/s00222-010-0302-7</a>"},"page":"75 - 119"}