FWF - Irrfahrten - Random versus deterministic: random walks and rotor walks

The goal of this project is to work in an interdisciplinary field at the confluent of different branches of Mathematics and to obtain synergy effects. The plan is to deepen the understanding of the interplay between properties of graphs and the behavior of two processes (a random process and its deterministic counterpart) on these graphs. The processes we consider are random walks and rotor walks (called also rotor-router walks), which are derandomized versions of random walks. In a variety of respects, the rotor-router walk captures the mean behavior of the random walk. On the other hand, these processes can also have very striking differences. The mathematics involved in this research is a mixture between probability theory, structure theory (algebra, geometry), graph theory, combinatorics, and has also connections with statistical physics.