The Annals of Applied Probability

Concentration of permanent estimators for certain large matrices

Shmuel Friedland, Brian Rider, and Ofer Zeitouni

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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.

Article information

Source
Ann. Appl. Probab., Volume 14, Number 3 (2004), 1559-1576.

Dates
First available in Project Euclid: 13 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1089736296

Digital Object Identifier
doi:10.1214/105051604000000396

Mathematical Reviews number (MathSciNet)
MR2071434

Zentralblatt MATH identifier
1082.15036

Subjects
Primary: 15A52

Keywords
Permanent concentration of measure random matrices

Citation

Friedland, Shmuel; Rider, Brian; Zeitouni, Ofer. Concentration of permanent estimators for certain large matrices. Ann. Appl. Probab. 14 (2004), no. 3, 1559--1576. doi:10.1214/105051604000000396. https://projecteuclid.org/euclid.aoap/1089736296


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