论文标题
开放kpz方程的成真结果
Ergodicity results for the open KPZ equation
论文作者
论文摘要
我们提供了新的存在证明，以及[0,1]上开放式KPZ方程的不变度度量的两个证明，以实现不均匀的Neumann边界数据的所有可能选择。两种证明都产生指数收敛的结果，当与[Knizel-Matetski，Arxiv：2211.04466]中建立的强feller特性结合使用时，会导致总变化。两种证明的重要成分是马尔可夫操作员构建紧凑的状态空间，该空间可衡量，其中包含所有通常的Hölder空间Modulo常数。一路上，强大的砍伐属性扩展到了较大的初始条件。这些参数不依赖于不变度量的确切描述，其中一些结果概括为空间颜色的噪声和其他边界条件的情况。
We give a new proof of existence as well as two proofs of uniqueness of the invariant measure of the open-boundary KPZ equation on [0,1], for all possible choices of inhomogeneous Neumann boundary data. Both proofs yield an exponential convergence result in total variation when combined with the strong Feller property which was recently established in [Knizel-Matetski, arXiv:2211.04466]. An important ingredient in both proofs is the construction of a compact state space for the Markov operator to act on, which measurably contains all of the usual Hölder spaces modulo constants. Along the way, the strong Feller property is extended to this larger class of initial conditions. The arguments do not rely on exact descriptions of the invariant measures, and some of the results generalize to the case of a spatially colored noise and other boundary conditions.
