On the function TreH+itK

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.