Nina Gantert (TUM):
Biased random walk on dynamical percolation
Zeit und Ort
Donnerstag, 7.11.24, 15:00-16:00, Hörsaal II, Albertstr. 23b
Zusammenfassung
As an example for a random walk in random environment, we study biased random walk for dynamical percolation on the d-dimensional lattice. We establish a law\nof large numbers and an invariance principle for this random walk using regeneration times.\nMoreover, we verify that the Einstein relation holds, and we investigate the speed of the walk\nas a function of the bias. While for d = 1 the speed is increasing, we show that in general this\nfails in dimension d ≥ 2. As our main result, we establish two regimes of parameters, separated\nby a critical curve, such that the speed is either eventually strictly increasing or eventually\nstrictly decreasing. This is in sharp contrast to the biased random walk on a static supercritical\npercolation cluster, where the speed is known to be eventually zero.\n\nBased on joint work with Sebastian Andres, Dominik Schmid and Perla Sousi.