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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Chakhtoun, Omar"],"institution":"The Graduate School and University Center of The City University of New York","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Elena Kosygina"],"committee_chairs":[],"committee_members":["Louis-Pierre Arguin","Olympia Hadjiliadis","Jay Rosen"],"year":2019,"date_issued":"2019-02-01T08:00:00Z","date_published":"2019-02-01T08:00:00Z","updated_at":"2026-07-24T02:00:35Z","subjects":["Probability","random walks","excited random walks","cookie walks","large deviations","diffusion approximation","branching processes"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://academicworks.cuny.edu/gc_etds/3030","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Elena Kosygina"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Louis-Pierre Arguin","Olympia Hadjiliadis","Jay Rosen"]},{"key":"dc:creator","label":"Author","values":["Chakhtoun, Omar"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2018-12-24T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["The Graduate School and University Center of The City University of New York"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Probability","random walks","excited random walks","cookie walks","large deviations","diffusion approximation","branching processes"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://academicworks.cuny.edu/gc_etds/3030"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["One-Dimensional Excited Random Walk with Unboundedly Many Excitations Per Site"]}]}],"canonical_facts":{"dc:contributor.advisor":["Elena Kosygina"],"dc:contributor.committeemember":["Louis-Pierre Arguin","Olympia Hadjiliadis","Jay Rosen"],"dc:creator":["Chakhtoun, Omar"],"dc:date.available":["2018-12-24T08:00:00Z"],"dc:description.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.
"],"dc:identifier":["https://academicworks.cuny.edu/gc_etds/3030"],"dc:subject":["Probability","random walks","excited random walks","cookie walks","large deviations","diffusion approximation","branching processes"],"dc:title":["One-Dimensional Excited Random Walk with Unboundedly Many Excitations Per Site"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["The Graduate School and University Center of The City University of New York"]},"updated_at":"2026-07-24T02:00:35Z"}