joint work of Michael Drmota, Walter Schachermayer and Josef Teichmann

Abstract: We show the first non-trivial (positive) result on the BMV-conjecture in dimension 3: first a representation of the BMV-measure in the spirit of Feynman-Kac formuals is presented. This approach does not yield new results, but a stochastic re-interpretation of the well-known Dyson expansion. It finally leads to a particular way how to sum up the Dyson series. Second we show by hypergeometric reasonings, that the BMV-measure is seen to be non-negative in several three dimensional cases. Integral Representation of the BMV-measure are presented.