发表机构
Courant Institute of Mathematical Sciences, New York University; Department of Mathematics, University of Maine（纽约大学库朗数学科学研究所; 缅因大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明一大类满足线性流性质的离散与连续模型在扩散标度下收敛到临界二维随机热流，建立了普适性结果。
AI 中文摘要
对于一大类满足线性流性质的离散时间和连续时间模型，我们证明了在空间和时间的扩散尺度下，它们收敛到临界二维随机热流。收敛是在测度值随机流空间中的有限维分布意义下成立的。我们考虑的离散模型类别包括具有有限程跳跃的时空随机环境中的随机游走，以及具有有限程空间相关的定向聚合物模型。我们考虑的连续模型类别包括几类不同的线性-乘性随机偏微分方程，其驱动噪声为高斯噪声，且具有光滑且紧支撑的协方差核。
英文摘要
For a large class of discrete- and continuous-time models satisfying a linear flow property, we prove convergence to the critical $2d$ stochastic heat flow under diffusive scaling of space and time. Convergence is in the sense of finite-dimensional distributions in the space of measure-valued stochastic flows. The class of discrete models we consider includes random walks in space-time random environments with finite-range jumps, and directed polymer models with finite-range spatial correlations. The class of continuum models we consider includes several distinct types of linear-multiplicative stochastic PDEs whose driving noise is Gaussian with a smooth and compactly supported covariance kernel.
Comments86 pages, comments welcome
