--- res: bibo_abstract: - We consider the stochastic quantization of a quartic double-well energy functional in the semiclassical regime and derive optimal asymptotics for the exponentially small splitting of the ground state energy. Our result provides an infinite-dimensional version of some sharp tunneling estimates known in finite dimensions for semiclassical Witten Laplacians in degree zero. From a stochastic point of view it proves that the L2 spectral gap of the stochastic one-dimensional Allen-Cahn equation in finite volume satisfies a Kramers-type formula in the limit of vanishing noise. We work with finite-dimensional lattice approximations and establish semiclassical estimates which are uniform in the dimension. Our key estimate shows that the constant separating the two exponentially small eigenvalues from the rest of the spectrum can be taken independently of the dimension.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Morris foaf_name: Brooks, Morris foaf_surname: Brooks foaf_workInfoHomepage: http://www.librecat.org/personId=B7ECF9FC-AA38-11E9-AC9A-0930E6697425 orcid: 0000-0002-6249-0928 - foaf_Person: foaf_givenName: Giacomo foaf_name: Di Gesù, Giacomo foaf_surname: Di Gesù bibo_doi: 10.1016/j.jfa.2021.109029 bibo_issue: '3' bibo_volume: 281 dct_date: 2021^xs_gYear dct_identifier: - UT:000644702800005 dct_isPartOf: - http://id.crossref.org/issn/0022-1236 - http://id.crossref.org/issn/1096-0783 dct_language: eng dct_publisher: Elsevier@ dct_title: Sharp tunneling estimates for a double-well model in infinite dimension@ ...