Another look at the Bal\'azs-Quastel-Sepp\"al\"ainen theorem
Another look at the Bal\'azs-Quastel-Sepp\"al\"ainen theorem
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发表时间：
2022-03
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通讯作者：
Yu Gu;T. Komorowski
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作者：
Yu Gu;T. Komorowski
。我们研究了具有1 + 1−维时空白噪声的KPZ方程，从平衡点出发，给出了[4]的主要结果的不同证明，即在t时刻解的方差为t2 / 3阶。而不是使用离散逼近通过排斥过程和第二类粒子，我们利用连接到定向聚合物在随机环境。在此过程中，我们证明了平稳连续定向聚合物的退火密度等于平稳随机Burgers方程的两点协方差函数，证实了[25]中的物理预测。
. 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 [4], 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 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 [25].