The two-dimensional KPZ equation in the entire subcritical regime
The two-dimensional KPZ equation in the entire subcritical regime
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DOI：
10.1214/19-aop1383
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发表时间：
2018-12
期刊：
影响因子：
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通讯作者：
F. Caravenna;Rongfeng Sun;Nikos Zygouras
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文献类型：
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作者：
F. Caravenna;Rongfeng Sun;Nikos Zygouras
我们考虑时空白色噪声驱动下的二维KPZ方程。我们在以前的工作中表明，如果噪声在空间尺度上被软化，其强度被标度为，则会发生具有显式临界点的转变。最近Chatterjee和Dunlap表明，该解决方案承认连续标度限制为，足够小。我们在这里证明，极限存在于整个亚临界制度，我们确定它作为一个添加剂的随机热方程的解决方案，建立所谓的爱德华-威尔金森波动。对于空间维为2的随机环境中的定向聚合物模型，同样的结果也成立。
We consider the KPZ equation in space dimension 2 driven by space-time white noise. We showed in previous work that if the noise is mollified in space on scale and its strength is scaled as , then a transition occurs with explicit critical point . Recently Chatterjee and Dunlap showed that the solution admits subsequential scaling limits as , for sufficiently small . We prove here that the limit exists in the entire subcritical regime and we identify it as the solution of an additive Stochastic Heat Equation, establishing so-called Edwards-Wilkinson fluctuations. The same result holds for the directed polymer model in random environment in space dimension 2.