## Biased random walk on dynamical percolation |

## Nina Gantert (TUM) |

## Thursday, 2024-11-07 15:00 |

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 of large numbers and an invariance principle for this random walk using regeneration times. Moreover, we verify that the Einstein relation holds, and we investigate the speed of the walk as a function of the bias. While for d = 1 the speed is increasing, we show that in general this fails in dimension d ≥ 2. As our main result, we establish two regimes of parameters, separated by a critical curve, such that the speed is either eventually strictly increasing or eventually strictly decreasing. This is in sharp contrast to the biased random walk on a static supercritical percolation cluster, where the speed is known to be eventually zero. Based on joint work with Sebastian Andres, Dominik Schmid and Perla Sousi. |