International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 7, Pages 389-393

On the function TreH+itK

Mark Fannes1 and Dénes Petz2

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.


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 tτ(exp(a+itb)) is positive definite. This shows that the Bessis-Moussa-Vilani conjecture holds for large random matrices in an asymptotic sense.