Open Access
Translator Disclaimer
August 2004 Concentration of permanent estimators for certain large matrices
Shmuel Friedland, Brian Rider, Ofer Zeitouni
Ann. Appl. Probab. 14(3): 1559-1576 (August 2004). DOI: 10.1214/105051604000000396

Abstract

Let $A_n=(a_{ij})_{i,j=1}^n$ be an $n×n$ positive matrix with entries in $[a,b], 0<a≤b$. Let $X_{n}=(\sqrt{a_{ij}}x_{ij})_{i,j=1}^{n}$ be a random matrix, where $\{x_{ij}\}$ are i.i.d. $N(0,1)$ random variables. We show that for large $n$, $\det (X_{n}^{T}X_{n})$ concentrates sharply at the permanent of $A_n$, in the sense that $n^{-1}\log (\det(X_{n}^{T}X_{n})/\operatorname {per}A_{n})\to_{n\to\infty}0$ in probability.

Citation

Download Citation

Shmuel Friedland. Brian Rider. Ofer Zeitouni. "Concentration of permanent estimators for certain large matrices." Ann. Appl. Probab. 14 (3) 1559 - 1576, August 2004. https://doi.org/10.1214/105051604000000396

Information

Published: August 2004
First available in Project Euclid: 13 July 2004

zbMATH: 1082.15036
MathSciNet: MR2071434
Digital Object Identifier: 10.1214/105051604000000396

Subjects:
Primary: 15A52

Keywords: concentration of measure , permanent , random matrices

Rights: Copyright © 2004 Institute of Mathematical Statistics

JOURNAL ARTICLE
18 PAGES


SHARE
Vol.14 • No. 3 • August 2004
Back to Top