Abstract
We study spectral Galerkin approximations of an Allen–Cahn equation over the twodimensional torus perturbed by weak spacetime white noise of strength ε√. We introduce a Wick renormalisation of the equation in order to have a system that is welldefined as the regularisation is removed. We show sharp upper and lower bounds on the transition times from a neighbourhood of the stable configuration −1 to the stable configuration 1 in the asymptotic regime ε→0. These estimates are uniform in the discretisation parameter N, suggesting an Eyring–Kramers formula for the limiting renormalised stochastic PDE. The effect of the “infinite renormalisation” is to modify the prefactor and to replace the ratio of determinants in the finitedimensional Eyring–Kramers law by a renormalised Carleman–Fredholm determinant.
Original language  English 

Pages (fromto)  127 
Number of pages  27 
Journal  Electronic Journal of Probability 
Volume  22 
Issue number  0 
DOIs  
Publication status  Published  28 Apr 2017 
Fingerprint Dive into the research topics of 'An Eyring–Kramers law for the stochastic Allen–Cahn equation in dimension two'. Together they form a unique fingerprint.
Profiles

Hendrik Weber
 Department of Mathematical Sciences  Professor of Probability
 Probability Laboratory at Bath
Person: Research & Teaching