Spectral properties of random triangular matrices

Details Spectral properties of random triangular matrices Spectral properties of random triangular matrices

2011-10-05

arxiv.org/abs/1110.1062v2

Mathematics

Probability

25 pages, 5 figures, Typos corrected. Expanded version. New result about support of LSD added

Scientific paper

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.

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