Work

The asymptotic distribution of the condition number for random circulant matrices

Year: 2022

Type: article

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 $$\textit{condition number}$$ condition number converges in distribution to a Fréchet law as the dimension of the matrix increases.

Source: Extremes

DOI: 10.1007/s10687-022-00442-w

Authors: Gerardo Barrera, Paulo Manrique-Mirón

Institutions: University of Helsinki, Instituto Politécnico Nacional

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,780

Funders: Helsingin Yliopisto, Helsingin ja Uudenmaan Sairaanhoitopiiri, Academy of Finland