Let An=(aij)i,j=1n be an n×n positive matrix with entries in [a,b], 0ij} 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 An, in the sense that $n^{-1}\log (\det(X_{n}^{T}X_{n})/\operatorname {per}A_{n})\to_{n\to\infty}0$ in probability.
Publié le : 2004-08-14
Classification:
Permanent,
concentration of measure,
random matrices,
15A52
@article{1089736296,
author = {Friedland, Shmuel and Rider, Brian and Zeitouni, Ofer},
title = {Concentration of permanent estimators for certain large matrices},
journal = {Ann. Appl. Probab.},
volume = {14},
number = {1},
year = {2004},
pages = { 1559-1576},
language = {en},
url = {http://dml.mathdoc.fr/item/1089736296}
}
Friedland, Shmuel; Rider, Brian; Zeitouni, Ofer. Concentration of permanent estimators for certain large matrices. Ann. Appl. Probab., Tome 14 (2004) no. 1, pp. 1559-1576. http://gdmltest.u-ga.fr/item/1089736296/