Asymptotic Positivity of Hurwitz Product Traces

2008/04/23 by Christian Fleischhack, Fleischhack, Christian · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Algebra and Logic #Formal Methods in Verification #Polynomial and algebraic computation #math-ph #math.MP #msc:15A24 #msc:15A45 #msc:15A48 #msc:44A10 #msc:49J40

paper · pdf · doi:10.48550/arxiv.0804.3665

18 pages, LaTeX

arxiv created 2008/04/23 · arxiv updated 2009/12/01

Abstract

Consider the polynomial tr (A + tB)^m in t for positive hermitian matrices A and B with m ∈ \N. The Bessis-Moussa-Villani conjecture (in the equivalent form of Lieb and Seiringer) states that this polynomial has nonnegative coefficients only. We prove that they are at least asymptotically positive, for the nontrivial case of AB ≠ 0. More precisely, we show that the k-th coefficient is positive for all integer m ≥ m₀, where m₀ depends on A, B and k.

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