Sharp tunneling estimates for a double-well model in infinite dimension

We consider the stochastic quantization of a quartic double-well energy functional in semiclassical regime and derive optimal asymptotics for exponentially small splitting ground state energy. Our result provides an infinite-dimensional version some sharp tunneling estimates known finite dimensions Witten Laplacians degree zero. From point view it proves that L2 spectral gap one-dimensional Allen-Cahn equation volume satisfies Kramers-type formula limit vanishing noise. work with finite-dimensional lattice approximations establish which are uniform dimension. key estimate shows constant separating two eigenvalues from rest spectrum can be taken independently