论文标题
1d kPz方程的不变性原理
An invariance principle for the 1D KPZ equation
论文作者
论文摘要
考虑一个离散的一维随机表面，该表面的高度在相邻点加上高度的函数以及独立的随机噪声。假设该函数在恒定偏移下是均衡的，在其参数中对称，并且在起源的邻域中至少是六倍，我们表明，随着噪声的差异为零，在适当的空间和时间尺度下，任何此类过程都会收敛到1d kpz方程的Cole-HOPF解决方案。本着唐斯克（Donsker）的不变性原则，这是1d kpz方程的不变原理。
Consider a discrete one-dimensional random surface whose height at a point grows as a function of the heights at neighboring points plus an independent random noise. Assuming that this function is equivariant under constant shifts, symmetric in its arguments, and at least six times continuously differentiable in a neighborhood of the origin, we show that as the variance of the noise goes to zero, any such process converges to the Cole-Hopf solution of the 1D KPZ equation under a suitable scaling of space and time. This proves an invariance principle for the 1D KPZ equation, in the spirit of Donsker's invariance principle for Brownian motion.
