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 \({\Phi^4_2}\) quantum field on the torus in terms of its density under translation. We also deduce that the \({\Phi^4_2}\) quantum field on the torus is an extreme point in the set of all L-symmetrizing measures, where L is the corresponding generator.
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Communicated by M. Hairer
Research supported in part by NSFC (Nos. 11401019, 11671035), the Fundamental Research Funds for the Central Universities (2014RC008), and DFG through CRC 701.
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Röckner, M., Zhu, R. & Zhu, X. Ergodicity for the Stochastic Quantization Problems on the 2D-Torus. Commun. Math. Phys. 352, 1061–1090 (2017). https://doi.org/10.1007/s00220-017-2865-2
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DOI: https://doi.org/10.1007/s00220-017-2865-2