Proof of the BMV Conjecture

Herbert R. Stahl

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arXiv · 1107.4875

Proof of the BMV Conjecture

Herbert R. Stahl

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Abstract

We prove the BMV (Bessis, Moussa, Villani, 1975) conjecture, which states that the function t -> Tr exp(A-tB), t \geq 0, is the Laplace transform of a positive measure on [0,\infty) if A and B are n x n Hermitian matrices and B is positive semidefinite. A semi-explicit representation for this measure is given.

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Herbert R. Stahl. 2011-07-25. Proof of the BMV Conjecture. https://arxiv.org/abs/1107.4875

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