Equivalent forms of the Bessis-Moussa-Villani conjecture

Details Equivalent forms of the Bessis-Moussa-Villani conjecture Equivalent forms of the Bessis-Moussa-Villani conjecture

2002-10-13

arxiv.org/abs/math-ph/0210027v3

J. Stat. Phys. 115, 185-190 (2004)

Physics

Mathematical Physics

LaTeX2e, 6 pages; additional explanations and dedication added; add. reference added

Scientific paper

The BMV conjecture for traces, which states that $Tr exp(A -\lambda B)$ is the Laplace transform of a positive measure, is shown to be equivalent to two other statements: (i) The polynomial $\lambda\mapsto Tr(A+\lambda B)^p$ has only non-negative coefficients for all $A, B \geq 0$, $p\in N$ and (ii) $\lambda\mapsto \Tr (A+\lambda B)^{-p}$ is the Laplace transform of a positive measure for $A, B \geq 0$, $p>0$.

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