On the lower bound of the refined Bessis--Moussa--Villani conjecture: proof of the cases S_{6,3} and S_{7,3} for 3x3 matrices

Daniel Hägele

For Hermitian matrices $\alpha ,\beta$ let $\A_{n,m}(e^α,e^β)$ be the average of the traces of all words with $n$ letters $e^{\alpha }$ and $m$ letters $e^{\beta }$. The refined Bessis--Moussa--Villani con…