Central limit theorem for a tagged particle in asymmetric simple exclusion

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• 作者：Patr&#xed ; cia Gon&#xe7 ; alves
• 关键词：Asymmetric exclusion ; Equilibrium fluctuations ; Boltzmann– ; Gibbs principle ; Tagged particle
• 刊名：Stochastic Processes and their Applications
• 出版年：2008
• 期刊代码：57_03044149
• 类别：mt
• 出版时间：March 2008
• 卷：118
• 期：3
• 页码：474-502
• 文件大小：436 K

摘要

We prove a functional central limit theorem for the position of a tagged particle in the one-dimensional asymmetric simple exclusion process for hyperbolic scaling, starting from a Bernoulli product measure conditioned to have a particle at the origin. We also prove that the position of the tagged particle at time t depends on the initial configuration, through the number of empty sites in the interval [0,(p−q)αt] divided by α, on the hyperbolic time scale and on a longer time scale, namely N^4/3.