# Bulk universality for generalized Wigner matrices

 Title: Bulk universality for generalized Wigner matrices Author: Erdos, Laszlo; Yau, Horng-Tzer; Yin, Jun Note: Order does not necessarily reflect citation order of authors. Citation: Erdos, László, Horng-Tzer Yau, and Jun Yin. 2011. “Bulk Universality for Generalized Wigner Matrices.” Probab. Theory Relat. Fields 154 (1-2) (October 6): 341–407. doi:10.1007/s00440-011-0390-3. http://dx.doi.org/10.1007/s00440-011-0390-3. Full Text & Related Files: 1001.3453v8.pdf (494.7Kb; PDF) Abstract: Consider $$N × N$$ Hermitian or symmetric random matrices H where the distribution of the (i, j) matrix element is given by a probability measure $$\nu_{ij}$$ with a subexponential decay. Let $$\sigma_{ij}^2$$ be the variance for the probability measure $$\nu_{ij}$$ with the normalization property that $$\sum_i\sigma_{ij}^2 = 1$$ for all j. Under essentially the only condition that $$c\leq N\sigma_{ij}^2 \leq c^{−1}$$ for some constant $$c > 0$$, we prove that, in the limit $$N \rightarrow \infty$$, 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 $$M^{−1}$$. Published Version: doi:10.1007/s00440-011-0390-3 Other Sources: http://arxiv.org/abs/1001.3453 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:25427234 Downloads of this work: