Random mass splitting and a quenched invariance principle

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• 作者：Sayan Banerjee^a ; ^{sayan.banerjee20@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Christopher Hoffman^b ; ^{hoffman@math.washington.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Random walk in random environment ; Invariance principle
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：126
• 期：2
• 页码：608-627
• 全文大小：277 K

文摘

We will investigate a random mass splitting model and the closely related random walk in a random environment (RWRE). The heat kernel for the RWRE at time tiner hidden">$t$ is the mass splitting distribution at tiner hidden">$t$. We prove a quenched invariance principle (QIP) for the RWRE which gives us a quenched central limit theorem for the mass splitting model. Our RWRE has an environment which is changing with time. We follow the outline for proving a QIP for a random walk in a space–time random environment laid out by Rassoul-Agha and Seppäläinen (2005) which in turn was based on the work of Kipnis and Varadhan (1986) and others.