{"issue":"4","title":"Bulk universality for Wigner Hermitian matrices with subexponential decay","publist_id":"4129","intvolume":"        17","extern":1,"publication_status":"published","publisher":"International Press","month":"07","page":"667 - 674","volume":17,"_id":"2763","quality_controlled":0,"type":"journal_article","citation":{"short":"L. Erdös, J. Ramírez, B. Schlein, T. Tao, V. Van, H. Yau, Mathematical Research Letters 17 (2010) 667–674.","ama":"Erdös L, Ramírez J, Schlein B, Tao T, Van V, Yau H. Bulk universality for Wigner Hermitian matrices with subexponential decay. <i>Mathematical Research Letters</i>. 2010;17(4):667-674.","mla":"Erdös, László, et al. “Bulk Universality for Wigner Hermitian Matrices with Subexponential Decay.” <i>Mathematical Research Letters</i>, vol. 17, no. 4, International Press, 2010, pp. 667–74.","ista":"Erdös L, Ramírez J, Schlein B, Tao T, Van V, Yau H. 2010. Bulk universality for Wigner Hermitian matrices with subexponential decay. Mathematical Research Letters. 17(4), 667–674.","ieee":"L. Erdös, J. Ramírez, B. Schlein, T. Tao, V. Van, and H. Yau, “Bulk universality for Wigner Hermitian matrices with subexponential decay,” <i>Mathematical Research Letters</i>, vol. 17, no. 4. International Press, pp. 667–674, 2010.","chicago":"Erdös, László, José Ramírez, Benjamin Schlein, Terence Tao, Vu Van, and Horng Yau. “Bulk Universality for Wigner Hermitian Matrices with Subexponential Decay.” <i>Mathematical Research Letters</i>. International Press, 2010.","apa":"Erdös, L., Ramírez, J., Schlein, B., Tao, T., Van, V., &#38; Yau, H. (2010). Bulk universality for Wigner Hermitian matrices with subexponential decay. <i>Mathematical Research Letters</i>. International Press."},"abstract":[{"text":"In this paper, we consider the ensemble of n×n Wigner Hermitian matrices H = (hℓk)1≤ℓ,k≤n that generalize the Gaussian unitary ensemble (GUE). The matrix elements hℓk = h̄ℓk are given by hℓk = n ?1/2(xℓk + √?1yℓk), where xℓk, yℓk for 1 ≤ ℓ &lt; k ≤ n are i.i.d. random variables with mean zero and variance 1/2, yℓ ℓ = 0 and xℓ ℓ have mean zero and variance 1. We assume the distribution of xℓk, yℓk to have subexponential decay. In [3], four of the authors recently established that the gap distribution and averaged k-point correlation of these matrices were universal (and in particular, agreed with those for GUE) assuming additional regularity hypotheses on the xℓk, yℓk. In [7], the other two authors, using a different method, established the same conclusion assuming instead some moment and support conditions on the xℓk, yℓk. In this short note we observe that the arguments of [3] and [7] can be combined to establish universality of the gap distribution and averaged k-point correlations for all Wigner matrices (with subexponentially decaying entries), with no extra assumptions.","lang":"eng"}],"author":[{"last_name":"Erdös","full_name":"László Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"José","full_name":"Ramírez, José A","last_name":"Ramírez"},{"first_name":"Benjamin","full_name":"Schlein, Benjamin","last_name":"Schlein"},{"full_name":"Tao, Terence","last_name":"Tao","first_name":"Terence"},{"last_name":"Van","full_name":"Van, Vu","first_name":"Vu"},{"last_name":"Yau","full_name":"Yau, Horng-Tzer","first_name":"Horng"}],"date_created":"2018-12-11T11:59:28Z","publication":"Mathematical Research Letters","status":"public","year":"2010","day":"01","date_published":"2010-07-01T00:00:00Z","date_updated":"2021-01-12T06:59:32Z"}