Spectral properties of random triangular matrices (Q2920374)
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scientific article; zbMATH DE number 6094185
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Spectral properties of random triangular matrices |
scientific article; zbMATH DE number 6094185 |
Statements
16 October 2012
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triangular matrices
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Wigner matrices
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Hankel matrices
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Toeplitz matrices
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symmetric circulant matrices
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limiting spectral distribution
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asymptotically free
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DT-operators
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Catalan words
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symmetric words
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semicircular law
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joint convergence of matrices
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Spectral properties of random triangular matrices (English)
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Inspired by the work of \textit{K. Dykema} and \textit{U. Haagerup} on their DT-operators in [Am. J. Math. 126, No. 1, 121--189 (2004; Zbl 1054.47026); J. Funct. Anal. 209, No. 2, 332--366 (2004; Zbl 1087.47006)], the authors study the moments of the limiting spectral distribution (LSD) of symmetric patterned triangular matrices with independent identically distributed (or with uniformly bounded moments) entries with mean 0 and variance 1, subject also to a technical condition on the link function.NEWLINENEWLINEThe last section of the paper is devoted to a discussion on other variants and absolute continuity.
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