SPECTRAL PROPERTIES OF RANDOM TRIANGULAR MATRICES
2012 ◽
Vol 01
(03)
◽
pp. 1250003
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Keyword(s):
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.
2010 ◽
Vol 101
(9)
◽
pp. 1927-1949
◽
Keyword(s):
1995 ◽
Vol 54
(2)
◽
pp. 295-309
◽
2019 ◽
Vol 08
(02)
◽
pp. 1950007
2014 ◽
Vol 03
(04)
◽
pp. 1450015
◽
1998 ◽
Vol 5
(2)
◽
pp. 423-432
1974 ◽
Vol 11
(01)
◽
pp. 63-71
◽
2013 ◽
Vol 44
(5)
◽
pp. 695-710