Bourgade, PaulYau, Horng-TzerYin, Jun2017-05-182013Bourgade, Paul, Horng-Tzer Yau, and Jun Yin. 2013. “Local Circular Law for Random Matrices.” http://dx.doi.org/10.1007/s00440-013-0514-z.0178-8051http://nrs.harvard.edu/urn-3:HUL.InstRepos:32706745The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of this law at any point zz away from the unit circle. More precisely, if ||z|−1|≥τ||z|−1|≥τ for arbitrarily small τ>0τ>0 , the circular law is valid around zz up to scale N−1/2+εN−1/2+ε for any ε>0ε>0 under the assumption that the distributions of the matrix entries satisfy a uniform subexponential decay condition.en-USLocal circular lawuniversalityJournal Article2017-05-1810.1007/s00440-013-0514-z