Communications in Mathematical Physics

, Volume 352, Issue 3, pp 1061–1090 | Cite as

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

  • Michael Röckner
  • Rongchan ZhuEmail author
  • Xiangchan Zhu


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Michael Röckner
    • 3
  • Rongchan Zhu
    • 1
    • 3
    Email author
  • Xiangchan Zhu
    • 2
    • 3
  1. 1.Department of MathematicsBeijing Institute of TechnologyBeijingChina
  2. 2.School of ScienceBeijing Jiaotong UniversityBeijingChina
  3. 3.Department of MathematicsUniversity of BielefeldBielefeldGermany

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