Concentration of permanent estimators for certain large matrices
概率论
2007-05-23 v1
摘要
Let A_n=(a_{ij})_{i,j=1}^n be an n\times n positive matrix with entries in [a,b], 0<a\le b. Let X_n=(\sqrta_{ij}x_{ij})_{i,j=1}^n be a random matrix, where {x_{ij}} are i.i.d. N(0,1) random variables. We show that for large n, \det (X_n^TX_n) concentrates sharply at the permanent of A_n, in the sense that n^{-1}\log (\det(X_n^TX_n)/perA_n)\to_{n\to\infty}0 in probability.
引用
@article{arxiv.math/0407139,
title = {Concentration of permanent estimators for certain large matrices},
author = {Shmuel Friedland and Brian Rider and Ofer Zeitouni},
journal= {arXiv preprint arXiv:math/0407139},
year = {2007}
}