Circulant type matrices with heavy tailed entries

Bose, Arup; Guha, S. R. D.; Hazra, Rajat Subhra; Saha, Koushik

doi:10.1016/j.spl.2011.07.001

Cited by 7 publications

(5 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For more results and application of circulant matrices, see also [14]. For recent progress on random circulant, reverse circulant matrices, we refer to [5], [7], [8], [9], [10], [29]. Hankel matrix is closely related to reverse circulant matrix and Toeplitz matrix.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Fluctuations of eigenvalues of patterned random matrices

Adhikari

Saha

2017

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

Abstract. In this article we study the fluctuation of linear statistics of eigenvalues of circulant, symmetric circulant, reverse circulant and Hankel matrices. We show that the linear spectral statistics of these matrices converge to the Gaussian distribution in total variation norm when the matrices are constructed using i.i.d. normal random variables. We also calculate the limiting variance of the linear spectral statistics for circulant, symmetric circulant and reverse circulant matrices.

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 99%

Fluctuations of eigenvalues of patterned random matrices

Adhikari

Saha

2017

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…The (random) circulant matrices and (random) circulant type matrices are an important object in different areas of pure and applied mathematics, for instance compressed sensing, cryptography, discrete Fourier transform, extreme value analysis, information processing, machine learning, numerical analysis, spectral analysis, time series analysis, etc. For more details we refer to (Aldrovandi 2001;Bose et al 2011Bose et al , 2012Davis 1994;Gray 2006; Kra and Simanca 2012;Rauhut 2009) and the monograph on random circulant matrices (Bose and Saha 2018). Some topics that have been studied are spectral norms, extremal distributions, the so-called limiting spectral distribution for random circulant matrices and random circulant-type matrices and process convergence of fluctuations, see (Bose et al 2002(Bose et al , 2009(Bose et al , 2010(Bose et al , 2011a(Bose et al , b, 2012a(Bose et al , b, 2020.…”

Section: Random Circulant Matricesmentioning

confidence: 99%

The asymptotic distribution of the condition number for random circulant matrices

Barrera

Manrique-Mirón

2022

Extremes

View full text Add to dashboard Cite

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.

show abstract

“…Note that = 1 or = + 1 yields the standard circulant matrix. If = − 1, then we obtain the so-called reverse circulant matrix [21].…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…There were discussions about the convergence in probability and distribution of the spectral norm of circulanttype matrices in [20]. The authors in [21] listed the limiting spectral distribution for a class of circulant-type matrices with heavy tailed input sequence. Ngondiep et al showed that the singular values of -circulants in [22].…”

Section: Introductionmentioning

confidence: 99%