On the function Tr e H + i t K

Mark Fannes and Dénes Petz

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 29, 1-5

Abstract:

We prove, for two free semicircularly distributed selfadjoint elements a and b in a type II 1 von Neumann algebra with faithful trace τ , that the function t ∈ ℝ ↦ τ ( exp ( a + i t b ) ) is positive definite. This shows that the Bessis-Moussa-Vilani conjecture holds for large random matrices in an asymptotic sense.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:759372

DOI: 10.1155/S0161171202011468

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