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We present estimates on the small singular values of a class of matrices withindependent Gaussian entries and inhomogeneous variance profile, satisfying abroad-connectedness condition. Using these estimates and concentration ofmeasure for the spectrum of Gaussian matrices with independent entries, weprove that for a large class of graphs satisfying an appropriate expansionproperty, the Barvinok--Godsil-Gutman estimator for the permanent achievessub-exponential errors with high probability.

Singular values of Gaussian matrices and permanent estimators