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math.PR2022
Directed mean curvature flow in noisy environment
Andris Gerasimovics, Martin Hairer, Konstantin Matetski
We consider the directed mean curvature flow on the plane in a weak Gaussian random environment. We prove that, when started from a sufficiently flat initial condition, a rescaled…
math.PR2015
Discretisations of rough stochastic PDEs
Martin Hairer, Konstantin Matetski
We develop a general framework for spatial discretisations of parabolic stochastic PDEs whose solutions are provided in the framework of the theory of regularity structures and whi…