Scaling limits of evolving spanning trees and of random walks on evolving spanning trees

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In this project we study scaling limits of evolving uniform spanning trees (UST) on further classes of networks (including Erdös-Renyi graphs, sequences of densely connected expander graphs and low-dimensional tori). The main motivation comes from modeling large and sparsely connected networks. Trees are the extreme cases of sparsely connected networks. In real world networks, the structure of the network might change over time. One emphasis of the project concerns a particular network dynamics. This is the Aldous-Broder algorithm which is a tree-valued stochastic process that generates the UST. A random walk is a simple stochastic process on a network which allows to explore the structure of the network. In the context of communication networks (e.g.\ internet, wifi) it can be understood as a message sent from device to device. In the current research random walks on dynamic network models are compared with random walks on static networks. In this project we determine the space and time scales on which the random walk has a diffusive scaling limit.