Stahl's Theorem (aka BMV Conjecture): Insights and Intuition on its Proof

Abstract

The Bessis-Moussa-Villani conjecture states that the trace of $\exp (A-tB)$ is, as a function of the real variable $t$, the Laplace transform of a positive measure, where $A$ and $B$ are respectively a hermitian and positive semi-definite matrix. The long standing conjecture was recently proved by Stahl and streamlined by Eremenko. We report on a more concise yet self-contained version of the proof.

arXiv commentConference paper

References in corpus (5)

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• On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices