论文标题
具有KPZ缩放的平均平均场样统计模型
Equilibrium mean-field-like statistical models with KPZ scaling
论文作者
论文摘要
我们已经考虑了涉及布朗游览的三个不同的“一体”统计系统，这些系统具有波动的kardar-parisi-zhang缩放，其关键指数$ν= \ frac {1} {3} $。在所有模型中，施加的外部约束将基本的随机过程推向了较大的偏差制度。具体而言，我们考虑了以下方面的波动：（i）在不均匀的有限树上进行的布朗段，线性生长的分支源于基质模型的Dumitriu-Edelman表示的平均场近似，（II）（1+1）（1+1）D“磁性” Dyck路径在有限的宽度（IIII）的Polimer radimed radimed radimer Rand中。在后一个问题中，切断了长期的空间波动，仅留下了拉伸路径的“典型”模式，我们确保键波动的kPz样缩放。相反，总结所有正常模式，我们获得了高斯行为。在所有考虑的模型中，KPZ在两个互补条件下都会出现：（i）将轨迹推向相空间的较大偏差区域，并且（ii）轨迹靠在无法穿透的边界上。
We have considered three different "one-body" statistical systems involving Brownian excursions, which possess for fluctuations Kardar-Parisi-Zhang scaling with the critical exponent $ν=\frac{1}{3}$. In all models imposed external constraints push the underlying stochastic process to a large deviation regime. Specifically, we have considered fluctuations for: (i) Brownian excursions on non-uniform finite trees with linearly growing branching originating from the mean-field approximation of the Dumitriu-Edelman representation of matrix models, (ii) (1+1)D "magnetic" Dyck paths within the strip of finite width, (iii) inflated ideal polymer ring with fixed gyration radius. In the latter problem cutting off the long-ranged spatial fluctuations and leaving only the "typical" modes for stretched paths, we ensure the KPZ-like scaling for bond fluctuations. To the contrary, summing up all normal modes, we get the Gaussian behavior. In all considered models, KPZ fluctuations emerge in presence of two complementary conditions: (i) the trajectories are pushed to a large deviation region of a phase space, and (ii) the trajectories are leaning on an impenetrable boundary.
