International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 7, Pages 389-393
doi:10.1155/S0161171202011468
On the function TreH+itK
1Instituut voor Theoretische Fysika, Katholieke Universiteit Leuven, Leuven B-3001, Belgium
2Department for Mathematical Analysis, Budapest University of Technology and Economics, Budapest XI. H-1521, Hungary
Received 21 January 2001
Copyright © 2002 Mark Fannes and Dénes Petz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We prove, for two free semicircularly distributed selfadjoint elements a and b in a type II1 von Neumann algebra with faithful trace τ, that the function t∈ℝ↦τ(exp(a+itb)) is positive definite. This shows that the Bessis-Moussa-Vilani conjecture holds for large random matrices in an asymptotic sense.