Interface evolution in bistable spatial models: a global approach
Thomas HUGHES
Université de Bath
Date(s) : 21/01/2025 iCal
14h30 - 15h30
We consider spatial stochastic population models exhibiting bistability. In such models, narrow interfaces tend to form between regions dominated by one of the two stable states. To understand how the population evolves, we may study the dynamics of these interfaces in time. For several bistable population models, including some variants of the voter model, it is known from recent work that the limiting interfaces, under certain rescalings, follow a geometric evolution called mean curvature flow. Surfaces evolving by mean curvature flow develop singularities in finite time, which imposes a short-time constraint and regularity assumptions on the convergence results.
In this talk, I will first discuss some models exhibiting this phenomenon, and results concerning their interfaces. I will then discuss a recent work which uses tools from analysis, in particular level-set methods and the theory of viscosity solutions, to improve upon recent interface convergence results for a broad class of bistable stochastic population models. In particular, we give checkable conditions on an ancestral dual process which guarantee that the interfaces converge globally in time to a generalized mean curvature flow.
This is joint work with Jessica Lin (McGill).
Emplacement
I2M Saint-Charles - Salle de séminaire
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