Ergodicity for the Stochastic Quantization Problems on the 2D-Torus

Michael Röckner; Rongchan Zhu; Xiangchan Zhu

doi:10.1007/s00220-017-2865-2

Ergodicity for the Stochastic Quantization Problems on the 2D-Torus

Michael Röckner, Rongchan Zhu^*, Xiangchan Zhu

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

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 Φ24 quantum field on the torus in terms of its density under translation. We also deduce that the Φ24 quantum field on the torus is an extreme point in the set of all L-symmetrizing measures, where L is the corresponding generator.

Original language	English
Pages (from-to)	1061-1090
Number of pages	30
Journal	Communications in Mathematical Physics
Volume	352
Issue number	3
DOIs	https://doi.org/10.1007/s00220-017-2865-2
Publication status	Published - 1 Jun 2017

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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 Φ24 quantum field on the torus in terms of its density under translation. We also deduce that the Φ24 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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N2 - 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 Φ24 quantum field on the torus in terms of its density under translation. We also deduce that the Φ24 quantum field on the torus is an extreme point in the set of all L-symmetrizing measures, where L is the corresponding generator.

AB - 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 Φ24 quantum field on the torus in terms of its density under translation. We also deduce that the Φ24 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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Ergodicity for the Stochastic Quantization Problems on the 2D-Torus

Abstract

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