On the Limit Distributions of Random Matrices with Independent or Free Entries

We state limit distribution results for random matrices with independent or free entries, also addressing when we get freeness in the limit and semicircular and circular limits. The results generalize some already known results about asymptotic freeness of large random matrices, but our goal is to get a more optimal flavour on these results. When having matrices with identically distributed entries, we show that freeness in the limit is natural when we have free entries, but unnatural when the entries are independent, and restricted to the case of circular limits.

Authors and Affiliations

1. Department of Mathematics, University of Oslo, P.O.B. 1053 Blindern, 0316 Oslo, Norway.¶E-mail: ryan@math.uio.no, , , , , , NO

   Øyvind Ryan

Received: 27 June 1997 / Accepted: 17 September 1997

Reprints and permissions