Weakly Asymmetric Non-Simple Exclusion Process and the Kardar–Parisi–Zhang Equation
Weakly Asymmetric Non-Simple Exclusion Process and the Kardar–Parisi–Zhang Equation
复制标题
弱不对称非简单排除过程和Kardar-Parisi-Zhang方程
DOI：
10.1007/s00220-015-2527-1
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发表时间：
2013
影响因子：
2.4
通讯作者：
N. Dawson
中科院分区：
文献类型：
--
作者：
Elizabeth R. Schell;K. McCracken;G. Scott;Jeff White;Philip Lavretsky;N. Dawson
通过推广Gärtner的离散Cole-Hopf变换(Stoch过程Appl，27：233-260,1987)，我们分析了一类非简单排斥过程和相应的增长模型。我们识别了主要的非线性，并通过施加梯度型条件来消除它。对于跳跃范围至多为3的情形，利用广义变换，证明了Kardar-Parisi-Zhang(KPZ)方程的排斥过程是收敛的。这是弱不对称性下关于相互作用粒子系统的第一个普适性结果。虽然这类排斥过程不是显式可解的，但在弱不对称性下，我们利用Amir等人的结果得到了阶跃初始条件的精确的一点极限分布。(普通纯应用数学，(4)：466-537,2011)和我们的收敛结果。
We analyze a class of non-simple exclusion processes and the corresponding growth models by generalizing the discrete Cole–Hopf transformation of Gärtner (Stoch Process Appl, 27:233–260, 1987). We identify the main non-linearity and eliminate it by imposing a gradient type condition. For hopping range at most 3, using the generalized transformation, we prove the convergence of the exclusion process toward the Kardar–Parisi–Zhang (kpz) equation. This is the first universality result under the weak asymmetry concerning interacting particle systems. While this class of exclusion processes are not explicitly solvable, under the weak asymmetry we obtain the exact one-point limiting distribution for the step initial condition by using the previous result of Amir et al. (Commun Pure Appl Math, 64(4): 466–537, 2011) and our convergence result.