International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 7, Pages 389-393
doi:10.1155/S0161171202011468
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
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.