Equivalent forms of the Bessis-Moussa-Villani conjecture

Elliott H. Lieb; Robert Seiringer

doi:10.1023/b:joss.0000019811.15510.27

Equivalent forms of the Bessis-Moussa-Villani conjecture

Elliott H. Lieb, Robert Seiringer

Mathematics

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

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)
Pages (from-to)	185-190
Number of pages	6
Journal	Journal of Statistical Physics
Volume	115
Issue number	1-2
DOIs	https://doi.org/10.1023/b:joss.0000019811.15510.27
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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10.1023/b:joss.0000019811.15510.27

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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.",

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AB - 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.

KW - BMV conjecture

KW - Laplace transform

KW - Padé approximants

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IS - 1-2

ER -

Equivalent forms of the Bessis-Moussa-Villani conjecture

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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