{"title":"Bulk universality for generalized Wigner matrices","page":"341 - 407","date_published":"2012-10-01T00:00:00Z","date_created":"2018-12-11T11:59:29Z","abstract":[{"lang":"eng","text":"Consider N × N Hermitian or symmetric random matrices H where the distribution of the (i, j) matrix element is given by a probability measure ν ij with a subexponential decay. Let σ ij 2 be the variance for the probability measure ν ij with the normalization property that Σ iσ i,j 2 = 1 for all j. Under essentially the only condition that c ≤ N σ ij 2 ≤ c -1 for some constant c &gt; 0, we prove that, in the limit N → ∞, the eigenvalue spacing statistics of H in the bulk of the spectrum coincide with those of the Gaussian unitary or orthogonal ensemble (GUE or GOE). We also show that for band matrices with bandwidth M the local semicircle law holds to the energy scale M -1. "}],"publisher":"Springer","month":"10","author":[{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"László Erdös"},{"last_name":"Yau","first_name":"Horng","full_name":"Yau, Horng-Tzer"},{"last_name":"Yin","first_name":"Jun","full_name":"Yin, Jun"}],"citation":{"short":"L. Erdös, H. Yau, J. Yin, Probability Theory and Related Fields 154 (2012) 341–407.","ama":"Erdös L, Yau H, Yin J. Bulk universality for generalized Wigner matrices. <i>Probability Theory and Related Fields</i>. 2012;154(1-2):341-407. doi:<a href=\"https://doi.org/10.1007/s00440-011-0390-3\">10.1007/s00440-011-0390-3</a>","chicago":"Erdös, László, Horng Yau, and Jun Yin. “Bulk Universality for Generalized Wigner Matrices.” <i>Probability Theory and Related Fields</i>. Springer, 2012. <a href=\"https://doi.org/10.1007/s00440-011-0390-3\">https://doi.org/10.1007/s00440-011-0390-3</a>.","apa":"Erdös, L., Yau, H., &#38; Yin, J. (2012). Bulk universality for generalized Wigner matrices. <i>Probability Theory and Related Fields</i>. Springer. <a href=\"https://doi.org/10.1007/s00440-011-0390-3\">https://doi.org/10.1007/s00440-011-0390-3</a>","mla":"Erdös, László, et al. “Bulk Universality for Generalized Wigner Matrices.” <i>Probability Theory and Related Fields</i>, vol. 154, no. 1–2, Springer, 2012, pp. 341–407, doi:<a href=\"https://doi.org/10.1007/s00440-011-0390-3\">10.1007/s00440-011-0390-3</a>.","ieee":"L. Erdös, H. Yau, and J. Yin, “Bulk universality for generalized Wigner matrices,” <i>Probability Theory and Related Fields</i>, vol. 154, no. 1–2. Springer, pp. 341–407, 2012.","ista":"Erdös L, Yau H, Yin J. 2012. Bulk universality for generalized Wigner matrices. Probability Theory and Related Fields. 154(1–2), 341–407."},"day":"01","date_updated":"2021-01-12T06:59:33Z","status":"public","extern":1,"_id":"2767","year":"2012","quality_controlled":0,"publication_status":"published","volume":154,"publist_id":"4123","intvolume":"       154","issue":"1-2","type":"journal_article","publication":"Probability Theory and Related Fields","doi":"10.1007/s00440-011-0390-3"}