Diffusivity and ballistic behavior of random walk in random environment

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Diffusivity and ballistic behavior of random walk in random environment

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Guo, Xiaoqin

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2012-09

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Abstract

In this thesis, we study the diffusive and ballistic behaviors of random walk in random environment (RWRE) in an integer lattice with dimension at least 2. Our contributions are in three directions: a conditional law of large numbers and regeneration structures for RWRE in Gibbsian environments, quenched invariance principles for balanced elliptic (but non uniformly elliptic) environments, and a proof of the Einstein relation for balanced iid uniformly elliptic environments.

Keywords

Einstein relation

Invariance principle

Limiting velocity

Random walk in random environment

Description

University of Minnesota Ph.D. dissertation. September 2012. Major: Mathematics. Advisor: Ofer Zeitouni. 1 computer file (PDF); iv, 104 pages, appendix A.

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Guo, Xiaoqin. (2012). Diffusivity and ballistic behavior of random walk in random environment. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/142482.

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