One-Dimensional Excited Random Walk with Unboundedly Many Excitations Per Site

Author

Omar Chakhtoun, The Graduate Center, City University of New YorkFollow

Date of Degree

2-2019

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Elena Kosygina

Committee Members

Louis-Pierre Arguin

Olympia Hadjiliadis

Jay Rosen

Subject Categories

Probability

Keywords

probability, random walks, excited random walks, cookie walks, large deviations, diffusion approximation, branching processes

Abstract

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.

Recommended Citation

Chakhtoun, Omar, "One-Dimensional Excited Random Walk with Unboundedly Many Excitations Per Site" (2019). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/3030