Date of Degree
probability, random walks, excited random walks, cookie walks, large deviations, diffusion approximation, branching processes
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.
Chakhtoun, Omar, "One-Dimensional Excited Random Walk with Unboundedly Many Excitations Per Site" (2019). CUNY Academic Works.