### Abstract

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

Original language | English (US) |
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Pages (from-to) | 185-190 |

Number of pages | 6 |

Journal | Journal of Statistical Physics |

Volume | 115 |

Issue number | 1-2 |

DOIs | |

State | Published - Apr 2004 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Keywords

- BMV conjecture
- Laplace transform
- Padé approximants

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## Cite this

Lieb, E. H., & Seiringer, R. (2004). Equivalent forms of the Bessis-Moussa-Villani conjecture.

*Journal of Statistical Physics*,*115*(1-2), 185-190. https://doi.org/10.1023/b:joss.0000019811.15510.27