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Random mass splitting and a quenched invariance principle

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  • Banerjee, Sayan
  • Hoffman, Christopher

Abstract

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 t is the mass splitting distribution at 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.

Suggested Citation

  • Banerjee, Sayan & Hoffman, Christopher, 2016. "Random mass splitting and a quenched invariance principle," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 608-627.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:2:p:608-627
    DOI: 10.1016/j.spa.2015.09.012
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    References listed on IDEAS

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    1. Boldrighini, C. & Minlos, R.A. & Pellegrinotti, A., 2009. "Discrete-time random motion in a continuous random medium," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3285-3299, October.
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