Singular values of Gaussian matrices and permanent estimators1. Issue 1 (30th July 2014) - Rudelson, Mark; Zeitouni, Ofer
ABSTRACT: We present estimates on the small singular values of a class of matrices with independent Gaussian entries and inhomogeneous variance profile, satisfying a broad‐connectedness condition. Using these estimates and concentration of measure for the spectrum of Gaussian matrices with independent entries, we prove that for a large class of graphs satisfying an appropriate expansion property, the Barvinok–Godsil‐Gutman estimator for the permanent achieves sub‐exponential errors with high probability. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 48, 183–212, 2016