Proof of the cases $p\le 7$ of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture

Abstract

It is shown that the polynomial $\lambda (t)=\mathrm{Tr}[(A+tB{)}^p]$ has nonnegative coefficients when $p\le 7$ and A and B are any two complex positive semidefinite $n\times n$ matrices with arbitrary $n$. This proofs a general nontrivial case of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture which is a long standing problem in theoretical physics.

5 pages; typos corrected; accepted for publication in Journal of Statistical Physics

Cited by in corpus (6)

• On D. Haegele's approach to the Bessis-Moussa-Villani conjecture
• Asymptotic Positivity of Hurwitz Product Traces
• Sums of Hermitian Squares as an Approach to the BMV Conjecture
• Asymptotic Positivity of Hurwitz Product Traces: Two Proofs
• Stahl's Theorem (aka BMV Conjecture): Insights and Intuition on its Proof
• On a polynomial positivity question of Collins, Dykema, and Torres-Ayala related to the Bessis-Moussa-Villani Conjecture