The asymptotic distribution of the condition number for random circulant matrices

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 appro...

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Bibliographic Details
Published in:Extremes (Boston) 2022-12, Vol.25 (4), p.567-594
Main Authors: Barrera, Gerardo, Manrique-Mirón, Paulo
Format: Article
Language:English
Subjects:
Civil Engineering
Convergence
Economics
Eigenvalues
Environmental Management
Finance
Hydrogeology
Insurance
Linear algebra
Management
Mathematics and Statistics
Quality Control
Random variables
Reliability
Safety and Risk
Statistics
Statistics for Business
Time series
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Summary: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.
ISSN:1386-1999
1572-915X
DOI:10.1007/s10687-022-00442-w