SPECTRAL PROPERTIES OF RANDOM TRIANGULAR MATRICES

DOI10.1142/S2010326312500037zbMath1258.60010arXiv1110.1062OpenAlexW2963964277MaRDI QIDQ2920374

Riddhipratim Basu, Shirshendu Ganguly, Rajat Subhra Hazra, Arup Bose

Publication date: 16 October 2012

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.1062

zbMATH Keywords

Toeplitz matricesWigner matricesHankel matriceslimiting spectral distributiontriangular matricesasymptotically freesemicircular lawCatalan wordssymmetric circulant matricesDT-operatorssymmetric wordsjoint convergence of matrices

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Free probability and free operator algebras (46L54) Random matrices (algebraic aspects) (15B52)

Related Items (3)

Bulk behavior of Schur–Hadamard products of symmetric random matrices ⋮ Unnamed Item ⋮ Limit theorems for free Lévy processes

Cites Work

• Convergence of joint moments for independent random patterned matrices
• Another look at the moment method for large dimensional random matrices
• Necessary and sufficient conditions for almost sure convergence of the largest eigenvalue of a Wigner matrix
• On the Lambert \(w\) function
• Multinomial identities arising from free probability theory.
• Limiting spectral distribution of a special circulant
• Invariant subspaces of the quasinilpotent DT-operator
• Limiting spectral distribution of \(XX^{\prime }\) matrices
• Distribution of eigenvalues of real symmetric palindromic Toeplitz matrices and circulant matrices
• Spectral measure of large random Hankel, Markov and Toeplitz matrices
• Distribution of eigenvalues for the ensemble of real symmetric Toeplitz matrices
• DT-operators and decomposability of Voiculescu's circular operator

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