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arXiv · 2110.03656

Boundary renormalisation of SPDEs

Máté Gerencsér·Martin Hairer
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Abstract

We consider the continuum parabolic Anderson model (PAM) and the dynamical $\Phi^4$ equation on the $3$-dimensional cube with boundary conditions. While the Dirichlet solution theories are relatively standard, the case of Neumann/Robin boundary conditions gives rise to a divergent boundary renormalisation. Furthermore for $\Phi^4_3$ a `boundary triviality' result is obtained: if one approximates the equation with Neumann boundary conditions and the usual bulk renormalisation, then the limiting process coincides with the one obtained using Dirichlet boundary conditions.

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Máté Gerencsér, Martin Hairer. 2021-10-07. Boundary renormalisation of SPDEs. https://doi.org/10.1080/03605302.2022.2109173

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