Singular Values of Gaussian Matrices and Permanent Estimators

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. (c) 2014 Wiley Periodicals, Inc.