Equivalent forms of the Bessis-Moussa-Villani conjecture

Elliott H. Lieb, Robert Seiringer

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


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 languageEnglish (US)
Pages (from-to)185-190
Number of pages6
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Apr 2004

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • BMV conjecture
  • Laplace transform
  • Padé approximants


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