Concentration of Random Determinants and Permanent Estimators

Abstract

We show that the absolute value of the determinant of a matrix with random independent (but not necessarily i.i.d.) entries is strongly concentrated around its mean. As an application, we show that Godsil–Gutman and Barvinok estimators for the permanent of a strictly positive matrix give subexponential approximation ratios with high probability. A positive answer to the main conjecture of the paper would lead to polynomial approximation ratios in the above problem.

Locations

• SIAM Journal on Discrete Mathematics - View
• arXiv (Cornell University) - View - PDF