Weakly Asymmetric Non-Simple Exclusion Process and the Kardar-Parisi-Zhang Equation
arXiv:1302.5760 · doi:10.1007/s00220-015-2527-1
Abstract
We analyze a class of non-simple exclusion processes and the corresponding growth models by generalizing Gaertners Cole-Hopf transformation. 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 concerning interacting particle systems in the context of KPZ universality class. While this class of exclusion processes are not explicitly solvable, we obtain the exact one-point limiting distribution for the step initial condition by using the previous result of Amir et al. (2011) and our convergence result.
32 pages, 1 figure. Comm. Math. Phys. in press. Reverted to v3 (i.e. v5 == v3) because v4 was a different paper that was mistakenly uploaded and should be ignored. v1 has errors; major changes made in v2
References in corpus (4)
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