Asymptotic *-moments of some random Vandermonde matrices
arXiv:1602.02815
Abstract
Appropriately normalized square random Vandermonde matrices based on independent random variables with uniform distribution on the unit circle are studied. It is shown that as the matrix sizes increases without bound, with respect to the expectation of the trace there is an asymptotic *-distribution, equal to that of a C[0,1]-valued R-diagonal element.
35 pages. Mathematica file available in consideration of computations of certain noncrossing cumulants. In version 1, Remark 2.1 was incorrect. This is corrected in version 2, where it is now Lemma 2.1. The proofs of Proposition 2.2 and several results in Section 4 were modified accordingly. Statements of these results remain the same, though they appear in different order