UVictoria Probability and Dynamics Seminar: Luca Michael Makowiec

We will introduce Random Spanning Trees in Random Environment (RSTRE), a disordered system on spanning trees that interpolates between the Uniform Spanning Tree (UST) and Minimum Spanning Tree (MST) measures. Our primary goal is to study how local and global observables of the RSTRE depend on the inverse temperature beta. Of particular interest is the diameter of a (typical) spanning tree, as it is the first step towards establishing convergence to a non-trivial scaling limit. Furthermore, for the RSTRE on the complete graph with uniform disorder, we discuss a sharp transition of the local limit of the RSTRE to either the UST or MST local limit. This stands in contrast to our conjectured smooth transition of the diameter when beta is inside the so-called intermediate regime.