论文标题
另一个看Balázs-Quastel-Seppäläinen定理
Another look at the Balázs-Quastel-Seppäläinen theorem
论文作者
论文摘要
我们以$ 1+1- $维空间白噪声为$ 1+1- $的KPZ方程式，以平衡开始，并给出了\ cite {bqs}的主要结果的不同证明，即，在时间$ t $的解决方案的方差是订单$ t^{2/3} $。我们没有通过排除过程和第二类粒子使用离散近似，而是在随机环境中使用与定向聚合物的连接。一路上，我们显示了固定连续性的导向聚合物的退火密度等于固定随机汉堡方程的两点协方差函数，从而证实了\ cite {mt}的物理预测。
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}.
