On the asymptotic spectral distribution of increasing size matrices: test functions, spectral clustering, and asymptotic estimates of outliers

• Published in: Linear algebra and its applications Vol. 697; pp. 615 - 638
• Main Authors: Bianchi, Davide, Garoni, Carlo
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.09.2024
• Subjects: Asymptotic spectral and singular value distribution; Hermitian block Toeplitz matrices; Outliers; Spectral clustering; Test functions; Urysohn's lemma and Tietze's extension theorem; Vague convergence of probability measures; Outliers; 47B06; Vague convergence of probability measures; Urysohn's lemma and Tietze's extension theorem; 15B05; 60B10; Spectral clustering; 15A60; Hermitian block Toeplitz matrices; Asymptotic spectral and singular value distribution; Test functions; 15A18

Let {An}n be a sequence of square matrices such that size(An)=dn→∞ as n→∞. We say that {An}n has an asymptotic spectral distribution described by a Lebesgue measurable function f:D⊂Rk→C if, for every continuous function F:C→C with bounded support,limn→∞⁡1dn∑i=1dnF(λi(An))=1μk(D)∫DF(f(x))dx, where μk...