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

DOI10.1007/s00220-017-2865-2zbMath1376.81045arXiv1606.02102OpenAlexW3099970161MaRDI QIDQ529631

Rong-Chan Zhu, Michael Roeckner, Xiang Chan Zhu

Publication date: 19 May 2017

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.02102

zbMATH Keywords

Markov semigroupergodicitystochastic quantizationstochastic mechanics

Mathematics Subject Classification ID

Markov semigroups and applications to diffusion processes (47D07) Quantization in field theory; cohomological methods (81T70) Constructive quantum field theory (81T08) Ergodic theorems, spectral theory, Markov operators (37A30) Transition functions, generators and resolvents (60J35) Stochastic mechanics (including stochastic electrodynamics) (81P20) Stochastic quantization (81S20)

Related Items (13)

Large \(N\) limit of the \(O(N)\) linear sigma model via stochastic quantization ⋮ Spectral gap for the stochastic quantization equation on the 2-dimensional torus ⋮ Existence of densities for the dynamic \(\Phi^4_3\) model ⋮ Unique ergodicity for a class of stochastic hyperbolic equations with additive space-time white noise ⋮ Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus ⋮ Concentration estimates for slowly time-dependent singular SPDEs on the two-dimensional torus ⋮ Weak universality of the dynamical \({{\Phi }_3^4}\) model on the whole space ⋮ Stochastic Heat Equations with Values in a Manifold via Dirichlet Forms ⋮ Kernel representation formula: from complex to real Wiener-Itô integrals and vice versa ⋮ Gibbs measures based on 1d (an)harmonic oscillators as mean-field limits ⋮ Conservative stochastic two-dimensional Cahn-Hilliard equation ⋮ Dirichlet form associated with the \(\Phi_3^4\) model ⋮ Classical field theory limit of many-body quantum Gibbs states in 2D and 3D

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