One-Dimensional Excited Random Walk with Unboundedly Many Excitations Per Site
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.
Probability, random walks, excited random walks, cookie walks, large deviations, diffusion approximation, branching processes
City University of New York - Graduate Center
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The Graduate School and University Center of The City University of New York