Boundary renormalisation of SPDEs

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 ${\Phi }_3^4$ 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.

51 pages

Cited by in corpus (4)

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• Singular SPDEs on Homogeneous Lie Groups
• Anderson Hamiltonians with singular potentials