[{"date_published":"2012-10-01T00:00:00Z","quality_controlled":0,"page":"341 - 407","publication":"Probability Theory and Related Fields","citation":{"apa":"Erdös, L., Yau, H., & Yin, J. (2012). Bulk universality for generalized Wigner matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-011-0390-3","ieee":"L. Erdös, H. Yau, and J. Yin, “Bulk universality for generalized Wigner matrices,” Probability Theory and Related Fields, 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.","short":"L. Erdös, H. Yau, J. Yin, Probability Theory and Related Fields 154 (2012) 341–407.","mla":"Erdös, László, et al. “Bulk Universality for Generalized Wigner Matrices.” Probability Theory and Related Fields, vol. 154, no. 1–2, Springer, 2012, pp. 341–407, doi:10.1007/s00440-011-0390-3.","chicago":"Erdös, László, Horng Yau, and Jun Yin. “Bulk Universality for Generalized Wigner Matrices.” Probability Theory and Related Fields. Springer, 2012. https://doi.org/10.1007/s00440-011-0390-3."},"day":"01","month":"10","uri_base":"https://research-explorer.ista.ac.at","dc":{"date":["2012"],"publisher":["Springer"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1007/s00440-011-0390-3"],"title":["Bulk universality for generalized Wigner matrices"],"source":["Erdös L, Yau H, Yin J. Bulk universality for generalized Wigner matrices. Probability Theory and Related Fields. 2012;154(1-2):341-407. doi:10.1007/s00440-011-0390-3"],"rights":["info:eu-repo/semantics/closedAccess"],"creator":["László Erdös","Yau, Horng-Tzer","Yin, Jun"],"description":["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 > 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. "],"identifier":["https://research-explorer.ista.ac.at/record/2767"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"]},"date_created":"2018-12-11T11:59:29Z","dini_type":"doc-type:article","date_updated":"2021-01-12T06:59:33Z","volume":154,"author":[{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Yau","first_name":"Horng"},{"last_name":"Yin","first_name":"Jun"}],"publication_status":"published","status":"public","intvolume":" 154","_id":"2767","extern":1,"abstract":[{"lang":"eng"}],"publist_id":"4123","issue":"1-2","type":"journal_article"}]