Ergodicity for the stochastic quantization problems on the 2D-torus

Abstract

In this paper we study the stochastic quantization problem on the two dimensional torus and establish ergodicity for the solutions. Furthermore, we prove a characterization of the ${\Phi }_2^4$ quantum field on the torus in terms of its density under translation. We also deduce that the ${\Phi }_2^4$ quantum field on the torus is an extreme point in the set of all $L$-symmetrizing measures, where $L$ is the corresponding generator.

arXiv admin note: text overlap with arXiv:1511.08030

References in corpus (1)

• An Eyring-Kramers law for the stochastic Allen-Cahn equation in dimension two

Cited by in corpus (3)

• Unique ergodicity for a class of stochastic hyperbolic equations with additive space-time white noise
• Construction of a non-Gaussian and rotation-invariant ${\Phi }^4$-measure and associated flow on ${\mathbb{R}}^3$ through stochastic quantization
• Concentration estimates for slowly time-dependent singular SPDEs on the two-dimensional torus