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The asymptotic distribution of the condition number for random circulant matrices.

The asymptotic distribution of the condition number for random circulant matrices.

Authors :
Barrera, Gerardo
Manrique-Mirón, Paulo
Source :
Extremes; Dec2022, Vol. 25 Issue 4, p567-594, 28p
Publication Year :
2022

Abstract

In this manuscript, we study the limiting distribution for the joint law of the largest and the smallest singular values for random circulant matrices with generating sequence given by independent and identically distributed random elements satisfying the so-called Lyapunov condition. Under an appropriated normalization, the joint law of the extremal singular values converges in distribution, as the matrix dimension tends to infinity, to an independent product of Rayleigh and Gumbel laws. The latter implies that a normalized condition number converges in distribution to a Fréchet law as the dimension of the matrix increases. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
13861999
Volume :
25
Issue :
4
Database :
Complementary Index
Journal :
Extremes
Publication Type :
Academic Journal
Accession number :
160049575
Full Text :
https://doi.org/10.1007/s10687-022-00442-w