Asymptotic Positivity of Hurwitz Product Traces

Details Asymptotic Positivity of Hurwitz Product Traces Asymptotic Positivity of Hurwitz Product Traces

2008-04-23

arxiv.org/abs/0804.3665v1

Physics

Mathematical Physics

18 pages, LaTeX

Scientific paper

Consider the polynomial $tr (A + tB)^m$ in $t$ for positive hermitian matrices $A$ and $B$ with $m \in \N$. 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 $AB \neq 0$. More precisely, we show that the $k$-th coefficient is positive for all integer $m \geq m_0$, where $m_0$ depends on $A$, $B$ and $k$.

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