The rotor walk is a deterministic analogue of the simple random walk. For any given graph, we construct a rotor configuration for which the escape rate of the corresponding rotor walk is equal to the escape rate of the simple random walk, and thus answer a question of Florescu, Ganguly, Levine, and Peres (2014).
"A rotor configuration with maximum escape rate." Electron. Commun. Probab. 25 1 - 5, 2020. https://doi.org/10.1214/20-ECP298