We prove uniform synchronization by noise with rates for the stochastic quantization equation in dimensions two and three. The proof relies on a combination of coming down from infinity estimates and the framework of order-preserving Markov semigroups derived in [O. Butkovsky and M. Scheutzow, Couplings via comparison principle and exponential ergodicity of SPDEs in the hypoelliptic setting, preprint (2019), arXiv:1907.03725]. In particular, it is shown that this framework can be applied to the case of state spaces given in terms of Hölder spaces of negative exponent.

中文翻译：

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维度2和3中的随机量化方程的噪声同步

对于二维和三维中的随机量化方程，我们证明了噪声与速率的均匀同步。证明依赖于从无穷大估计中得出的结果和[O.]中得出的保序马尔可夫半群的框架。Butkovsky和M. Scheutzow，在椭圆形环境中通过比较原理和SPDE的指数遍历性进行耦合，预印本（2019），arXiv：1907.03725]。特别地，表明该框架可以应用于以负指数的霍尔德空间给出的状态空间的情况。