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One-Dimensional Excited Random Walk With Unboundedly Many Excitations Per Site, Omar Chakhtoun
One-Dimensional Excited Random Walk With Unboundedly Many Excitations Per Site, Omar Chakhtoun
Dissertations, Theses, and Capstone Projects
We study a discrete time excited random walk on the integers lattice requiring a tail decay estimate on the number of excitations per site and extend the existing framework, methods, and results to a wider class of excited random walks.
We give criteria for recurrence versus transience, ballisticity versus zero linear speed, completely classify limit laws in the transient regime, and establish a functional limit laws in the recurrence regime.