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arXiv · 1606.02102

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

Michael Rockner·Rongchan Zhu·Xiangchan Zhu
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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 $Φ^4_2$ quantum field on the torus in terms of its density under translation. We also deduce that the $Φ^4_2$ 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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BibTeXRIS

Michael Rockner, Rongchan Zhu, Xiangchan Zhu. 2016-06-23. Ergodicity for the stochastic quantization problems on the 2D-torus. https://doi.org/10.1007/s00220-017-2865-2

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