Bulk behaviour of SchurHadamard products of symmetric random matrices
Abstract
We develop a general method for establishing the existence of the Limiting Spectral Distributions (LSD) of SchurHadamard products of independent symmetric patterned random matrices. We apply this method to show that the LSDs of SchurHadamard products of some common patterned matrices exist and identify the limits. In particular, the SchurHadamard product of independent Toeplitz and Hankel matrices has the semicircular LSD. We also prove an invariance theorem that may be used to find the LSD in many examples.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.2207
 Bibcode:
 2014arXiv1402.2207B
 Keywords:

 Mathematics  Probability;
 Primary 15B52;
 60B20;
 secondary 60B10;
 60F99;
 60B99
 EPrint:
 27 pages, 1 figure