The speed of biased random walks among dynamical random conductances

Abstract: We study biased random walks on dynamical random conductances on $\mathbb{Z}^d$. We analyze three models: the Variable Speed Biased Random Walk (VBRW), the Normalized VBRW (NVBRW), and the Constant Speed Biased Random Walk (CBRW). We prove positivity of the linear speed for all models and investigate how the speed depends on the bias $\lambda$. Notably, while the CBRW speed increases for large $\lambda$, the NVBRW speed can asymptotically decrease even in uniformly elliptic conductances. The results for NVBRW generalize the results proved for biased random walks on dynamical percolation in [1].