A hyper-geometric approach to the BMV-conjecture

TL;DR

This paper introduces a stochastic representation of the BMV-measure and demonstrates its positivity in three dimensions for specific cases using combinatorial techniques.

Contribution

It offers a new stochastic approach to the BMV-conjecture and proves measure positivity in dimension three for certain cases, advancing understanding of the conjecture.

Findings

Representation of BMV-measure via stochastic methods

Positivity of measures in dimension 3 for specific cases

Use of combinatorial methods to establish results

Abstract

We provide a representation of the (signed) BMV-measure by stochastic means and prove positivity of the respective measures in dimension $d=3$ in several non-trivial cases by combinatorial methods.