Abstract
In this paper, we investigate the stochastic mean curvature flow (SMCF) on networks, a niche area within stochastic processes and geometric anal- ysis. By applying Ito calculus, we analyze the evolution of network struc- tures influenced by random perturbations. We derive a stochastic differ- ential equation (SDE) for the network edges and utilize numerical simula- tions to study the stability, long-term behavior, and pattern formation in these systems. Our results offer new insights into the dynamics of com- plex networks under stochastic influences and open pathways for future research in stochastic geometry.
