再看Balázs-Quastel-Seppäläinen定理
Another look at the Balázs-Quastel-Seppäläinen theorem
摘要：
本文研究了具有$1+1-$维时空白噪声的KPZ方程，从平衡态出发，对\cite{bqs}的主要结果给出了不同的证明，即，解在时间$t$的方差为$t^{2/3}$阶。而不是使用一个离散逼近通过排它过程和第二类粒子，我们利用连接到定向聚合物在一个随机的环境。在此过程中，我们证明了稳态连续定向聚合物的退火密度等于稳态随机Burgers方程的两点协方差函数，证实了\cite{MT}中的物理预测。
英文摘要：
We study the KPZ equation with a $1+1-$dimensional spacetime white noise, started at equilibrium, and give a different proof of the main result of \cite{bqs}, i.e., the variance of the solution at time $t$ is of order $t^{2/3}$. Instead of using a discrete approximation through the exclusion process and the second class particle, we utilize the connection to directed polymers in a random environment. Along the way, we show the annealed density of the stationary continuum directed polymer equals to the two-point covariance function of the stationary stochastic Burgers equation, confirming the physics prediction in \cite{MT}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
