Spectral Properties of Random Cluster Models and Applications to Composite Materials

Explore the analytic continuation method for analyzing homogenization in disordered media through this 48-minute conference talk. Discover how this technique, originally developed for studying composites in materials science, leverages the spectral properties of random self-adjoint operators determined by fixed underlying geometry and random perturbations representing inhomogeneous materials. Learn about the intimate connections between these operators and the Gaussian Free Field and Uniform Spanning Tree, while examining recent results on spectral properties that have significantly enhanced existing numerical methods. Gain insights into multiple potential research directions in this intersection of probability theory and geometry, presented by Tom Alberts from the University of Utah at IPAM's New Interactions Between Probability and Geometry Workshop.