{"status":"public","abstract":[{"lang":"eng","text":"We consider N ×N Hermitian Wigner random matrices H where the probabilitydensity for each matrix element is given by the density v(x)=e-U(x). We prove that the eigenvalue statistics in the bulk are given by the Dyson sine kernel provided that U ∈ C 6(R{double-struck}) with at most polynomially growing derivatives and v(x)≤C e-c(x) for x large. The proof is based upon an approximate time reversal of the Dyson Brownian motion combined with the convergence of the eigenvalue density to the Wigner semicircle law on short scales."}],"date_published":"2010-07-01T00:00:00Z","type":"journal_article","publist_id":"4130","publication_status":"published","extern":1,"volume":63,"month":"07","publication":"Communications on Pure and Applied Mathematics","publisher":"Wiley-Blackwell","citation":{"mla":"Erdös, László, et al. “Bulk Universality for Wigner Matrices.” <i>Communications on Pure and Applied Mathematics</i>, vol. 63, no. 7, Wiley-Blackwell, 2010, pp. 895–925, doi:<a href=\"https://doi.org/10.1002/cpa.20317\">10.1002/cpa.20317</a>.","ista":"Erdös L, Ramírez J, Yau H, Péché S, Schlein B. 2010. Bulk universality for Wigner matrices. Communications on Pure and Applied Mathematics. 63(7), 895–925.","ieee":"L. Erdös, J. Ramírez, H. Yau, S. Péché, and B. Schlein, “Bulk universality for Wigner matrices,” <i>Communications on Pure and Applied Mathematics</i>, vol. 63, no. 7. Wiley-Blackwell, pp. 895–925, 2010.","short":"L. Erdös, J. Ramírez, H. Yau, S. Péché, B. Schlein, Communications on Pure and Applied Mathematics 63 (2010) 895–925.","chicago":"Erdös, László, José Ramírez, Horng Yau, Sandrine Péché, and Benjamin Schlein. “Bulk Universality for Wigner Matrices.” <i>Communications on Pure and Applied Mathematics</i>. Wiley-Blackwell, 2010. <a href=\"https://doi.org/10.1002/cpa.20317\">https://doi.org/10.1002/cpa.20317</a>.","ama":"Erdös L, Ramírez J, Yau H, Péché S, Schlein B. Bulk universality for Wigner matrices. <i>Communications on Pure and Applied Mathematics</i>. 2010;63(7):895-925. doi:<a href=\"https://doi.org/10.1002/cpa.20317\">10.1002/cpa.20317</a>","apa":"Erdös, L., Ramírez, J., Yau, H., Péché, S., &#38; Schlein, B. (2010). Bulk universality for Wigner matrices. <i>Communications on Pure and Applied Mathematics</i>. Wiley-Blackwell. <a href=\"https://doi.org/10.1002/cpa.20317\">https://doi.org/10.1002/cpa.20317</a>"},"page":"895 - 925","issue":"7","day":"01","year":"2010","_id":"2762","quality_controlled":0,"doi":"10.1002/cpa.20317","intvolume":"        63","author":[{"full_name":"László Erdös","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Ramírez","first_name":"José","full_name":"Ramírez, José A"},{"full_name":"Yau, Horng-Tzer","last_name":"Yau","first_name":"Horng"},{"last_name":"Péché","first_name":"Sandrine","full_name":"Péché, Sandrine"},{"last_name":"Schlein","first_name":"Benjamin","full_name":"Schlein, Benjamin"}],"date_created":"2018-12-11T11:59:28Z","date_updated":"2021-01-12T06:59:32Z","title":"Bulk universality for Wigner matrices"}