Mark Rudelson, Ofer Zeitouni
Published 2013-01-26, updated 2014-08-29Version 3
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.
Comments: small revision, no major changes. Changed terminology to "broadly connected". Corrected error in probability estimate in statement of theorems 1.4 and 1.5
Concentration of random determinants and permanent estimators
Concentration of permanent estimators for certain large matrices
On the largest Lyapunov exponent for products of Gaussian matrices
![QR code for arXiv:1301.6268 [math.PR]](http://oss.arxitics.com/images/favicon.svg)