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.

Conference paper

References in corpus (3)

• Proof of the cases $p\le 7$ of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture
• Further implications of the Bessis-Moussa-Villani conjecture
• On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices