BASU, RIDDHIPRATIM ; BOSE, ARUP ; GANGULY, SHIRSHENDU ; HAZRA, RAJAT SUBHRA (2012) Spectral properties of random triangular matrices Random Matrices: Theory and Applications, 01 (03). p. 1250003. ISSN 2010-3263
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Official URL: http://doi.org/10.1142/S2010326312500037
Related URL: http://dx.doi.org/10.1142/S2010326312500037
Abstract
We prove the existence of the limiting spectral distribution (LSD) of symmetric triangular patterned matrices and also establish the joint convergence of sequences of such matrices. For the particular case of the symmetric triangular Wigner matrix, we derive expression for the moments of the LSD using properties of Catalan words. The problem of deriving explicit formulae for the moments of the LSD does not seem to be easy to solve for other patterned matrices. The LSD of the non-symmetric triangular Wigner matrix also does not seem to be easy to establish.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to World Scientific Publishing Co Pte Ltd. |
| Keywords: | Triangular Matrices; Wigner. Hankel; Toeplitz And Symmetric Circulant Matrices; Limiting Spectral Distribution; Asymptotically Free; DT-Operators; Catalan Words; Symmetric Words; Semicircular Law; Joint Convergence Of Matrices. |
| ID Code: | 121106 |
| Deposited On: | 09 Jul 2021 08:53 |
| Last Modified: | 09 Jul 2021 08:53 |
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