Mahler Measures, Random Walks, and Asymptotics

Originally motivated by a question about the minimal Mahler measure among polynomials with a fixed Galois group, this work led to the computation of several multivariate Mahler measures. These admit a probabilistic  interpretation in terms of random walks in the plane and, in some cases, are also connected to densities of states in condensed matter physics. In this talk, I will explain how these probabilistic interpretations lead both to asymptotic formulas for these Mahler measures and to their high-precision numerical computation in certain cases. This is joint work with Gunther Cornelissen and David Hokken.