Singular values of Gaussian matrices and permanent estimators
Probability
2014-09-01 v3 Data Structures and Algorithms
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.
Cite
@article{arxiv.1301.6268,
title = {Singular values of Gaussian matrices and permanent estimators},
author = {Mark Rudelson and Ofer Zeitouni},
journal= {arXiv preprint arXiv:1301.6268},
year = {2014}
}
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