文章基本信息

标题：Ergodicity of the KPZ Fixed Point
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作者：Leandro P. R. Pimentel
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2021
卷号：18
期号：1
页码：963
DOI：10.30757/ALEA.v18-35
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：In this paper we consider the Kardar-Parisi-Zhang (KPZ) fixed point (ht , t ≥ 0) (Corwin et al., 2015; Matetski et al., 2016) and prove that, for suitable initial conditions, ht(x) − ht(0) converges to a two-sided Brownian motion with zero drift and diffusion coefficient 2, as t → ∞. The heart of the proof is the coupling method, that allows us to compare the TASEP height function started from a perturbation of density 1/2 with its invariant counterpart which, under KPZ scaling, turns into uniform estimates for the KPZ fixed point.