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

<p>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.</p> <p>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.</p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

The Graduate School and University Center of The City University of New York

Year dc:date.available

2019

Author dc:creator

• Chakhtoun, Omar

Advisor dc:contributor.advisor

• Elena Kosygina

Committee members dc:contributor.committeemember

• Louis-Pierre Arguin
• Olympia Hadjiliadis
• Jay Rosen

• Probability
• random walks
• excited random walks
• cookie walks
• large deviations
• diffusion approximation
• branching processes

Repository record dc:identifier

https://academicworks.cuny.edu/gc_etds/3030

OAI identifier oai:identifier

oai:academicworks.cuny.edu:gc_etds-4044