10.02.2025 16:30 Daniel Sharon (Technion, Haifa, Israel):
The Cluster Cluster ModelBC1 2.01.10 (8101.02.110) (Parkring 11, 85748 Garching-Hochbrück)
We consider a stochastic process on the graph $\mathds{Z}^d$. Each $x\in \mathds{Z}^d$ starts with a cluster of size 1 with probability $p \in (0,1]$ independently. Each cluster $C$ of performs a continuous time SRW with rate $\abs{C}^{-\alpha}$. If it attempts to move to a vertex occupied by another cluster, it does not move, and instead the two clusters connect via a new edge. Focusing on dimension $d=1$, we show that for $\alpha>-2$, at time $t$, the cluster size is of order $t^\frac{1}{\alpha + 2}$, and for $\alpha \le -2$ we get an infinite component. Additionally, for $\alpha = 0$ we show convergence in distribution of the scaling limit.