Perturbation of Wigner matrices and a conjecture 1 (2009)
Abstract Let H0 be an arbitrary self-adjoint n n matrix and H(n) be an n n (random) Wigner matrix. We show that t 7! Tr exp(H(n) itH0) is positive de nite in the average. This partially answers a...
On the function Tr exp(A + itB) 1 (2009)
We prove, for two free semicircularly distributed selfadjoint elements a and b in a type II1 von Neumann algebra with faithful trace, that the function t 2 R 7! (exp(a + itb)) is positive de nite....
On the function TreH+itK (2002)
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...