The Brownian net is a collection of branching-coalescing Brownian motions starting from every point in the space-time plane ℝ2, which is expected to be a universal scaling limit of one-dimensional interacting particle systems with branching-coalescence. However, it remains a challenge to show the convergence of models with crossing paths. We considered the convergence of branching and coalescing non-simple random walks so that the paths can cross. We use the duality between biased voter models and branching-coalescing random walks, and partially obtained the convergence result. Along the way, we showed that the equilibrium measure of the interface of the biased voter model is continuous with respect to the biased parameter.
This talk is based on joint works with Rongfeng Sun and Jan M. Swart.
Jinjiong Yu is a Postdoc at NYU Shanghai. He graduated from Peking University before obtaining his Ph.D. in mathematics at National University of Singapore in 2017. His main research interests lie in interacting particle systems and statistical mechanical models.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai