Synchronisation by noise for the stochastic quantisation equation in dimensions 2 and 3
- Authors: Benjamin Gess, Pavlos Tsatsoulis
- Preprint year: 2019
- First public date: 2019-10-17
- arXiv: 1910.07769
- Status: Published
- Publication type: Journal article
- Publication year: 2020
- Journal: Stochastics and Dynamics 20(6), 2040006 (2020)
- DOI: 10.1142/S0219493720400067
Abstract
We prove uniform synchronisation by noise with rates for the stochastic quantisation 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 [Butkovsky, Scheutzow; 2019]. 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.