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.
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