Brooks, M. (2019). Small noise spectral analysis for a bistable system in large dimensions [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2019.67982
In this thesis, I am studying the convergence rate to equilibrium of the stochastic Allen-Cahn equation, in the limit of vanishing noise. This convergence rate can be quantified by the spectral gap of the associated diffusion operator. It will be our primary goal, to compute the asymptotic behaviour of the spectral gap for the discretized version of the Allen-Cahn equation, with error terms uniformly controlled in the parameter N of the discrete model.