论文标题
通过规律性结构的空间危险GKPZ的收敛
Convergence of space-discretised gKPZ via Regularity Structures
论文作者
论文摘要
在这项工作中，我们展示了对广义kpz方程的离散表达$ \ partial_t u =（ΔU） + g（u）（\ nabla u）^2 + k（\ nabla u） + h（\ nabla u） + h（u） + f（u） + f（u） + f（u） + f（u）endeciian cor lap lapt use $ upt， $ \ nabla $是一个离散的梯度，而无需固定空间尺寸。我们的收敛结果是在Hairer和Erhard [Arxiv：1705.02836]引入的离散规律性结构中建立的。我们扩展了新想法，在[arxiv：2103.13479]中发现的收敛结果涉及由（重新定义的）对称简单排除过程驱动的抛物线式安德森模型的离散形式。这是第一次处理一个离散的广义KPZ方程，这是迈向一般收敛结果的主要一步，它将涵盖大型离散模型。
In this work, we show a convergence result for the discrete formulation of the generalised KPZ equation $\partial_t u = (Δu) + g(u)(\nabla u)^2 + k(\nabla u) + h(u) + f(u)ξ_t(x)$, where the $ξ$ is a real-valued random field, $Δ$ is the discrete Laplacian, and $\nabla$ is a discrete gradient, without fixing the spatial dimension. Our convergence result is established within the discrete regularity structures introduced by Hairer and Erhard [arXiv:1705.02836]. We extend with new ideas the convergence result found in [arXiv:2103.13479] that deals with a discrete form of the Parabolic Anderson model driven by a (rescaled) symmetric simple exclusion process. This is the first time that a discrete generalised KPZ equation is treated and it is a major step toward a general convergence result that will cover a large family of discrete models.
