25.07.2022 16:30 Viktor Bezborodov (Universität Göttingen):
Continuous-time frog model: linear spread and explosion.2.01.10 (Parkring 11, 85748 Garching-Hochbrück)

In this talk we consider a continuous-time frog model on Z^d. As the discrete-time random walk is a.s. bounded for every fixed time, the original discrete-time frog model grows linearly with time no matter how heavy-tailed the distribution of the number of sleeping frogs per site is. This is no longer the case for the continuous-time model, and we discuss conditions on the initial distribution μ (mu) of number of sleeping particles per site ensuring linear growth, faster than linear growth, or explosion. The proof technique is based on a comparison with certain percolation-type models such as totally asymmetric discrete Boolean percolation or greedy lattice animals. We also discuss how these techniques can be applied to similar stochastic growth models.