Interface tightness of biased voter models
speaker: Jan Swart (The Czech Academy of Sciences, Institute of Information Theory and Automation, Prague)abstract: It is well-known that (biased) voter models are dual to systems of (branching-) coalescing random walks. In the one-dimensional case, coalescing random walks have a diffusive scaling limit, which is the Brownian web. For nearest-neighbor random walks this was proved by Fontes, Isopi, Newman, and Ravishankar (2003), who built on work of Arratia (1979) and Tóth and Werner (1998). The case of long-range coalescing random walks was treated by Newman, Ravishankar and Sun (2005). For branching-coalescing random walks with weak branching, the scaling limit is the Brownian net. In the nearest-neighbor case, this was proved by Sun and myself (2008), but in the long-range case the problem is still open. In his PhD thesis (2017), Jinjiong Yu was able to solve the problem assuming tightness. In my talk, I will explain how the problem of proving tightness is related to the problem of proving interface tightness for biased voter models. For the latter problem, I will present recent progress of Sun, Yu and myself, which builds on earlier work of Cox and Durrett (1995), Belhaouari, Mountford and Valle (2007), and Sturm and myself (2008).
timetable:
Tue 2 Apr, 17:00 - 18:00, Aula Dini
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