{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/129438"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/129438","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Dimer models and limit shapes from different perspectives","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms","abstract_has_math":false,"creators":["Vu, Hieu Trung"],"institution":"University of Illinois Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Di Francesco, Philippe","Kedem, Rinat","Yong, Alexander","Russkikh, Marianna"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-05-01","date_published":"2025-05-01","updated_at":"2026-07-22T22:25:05Z","subjects":["Dimer models","limit shapes","arctic curves","statistical mechanics","discrete complex analysis"],"languages":["en","eng"],"rights":["Copyright 2025 Hieu Trung Vu"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/129438","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Di Francesco, Philippe","Kedem, Rinat","Yong, Alexander","Russkikh, Marianna"]},{"key":"dc:creator","label":"Author","values":["Vu, Hieu Trung"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-05-01","2025-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Dimer models","limit shapes","arctic curves","statistical mechanics","discrete complex analysis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2025 Hieu Trung Vu"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/129438"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms","The student, Hieu Trung Vu, accepted the attached license on 2025-04-23 at 19:43.","The student, Hieu Trung Vu, submitted this Dissertation for approval on 2025-04-23 at 19:50.","This Dissertation was approved for publication on 2025-05-01 at 08:49.","DSpace SAF Submission Ingestion Package generated from Vireo submission #21933 on 2025-10-19 at 18:18:55","This thesis considers two projects and some progress toward the theory of dimer models in statistical mechanics. The two questions we are trying to answer are the limit shapes of the dimer model and the height function fluctuation in the scaling limit. The first project considers the asymptotic and arctic curves of dimer models arising from a special set of initial data of the octahedron recurrence. This is a joint work with Di Francesco. This approach of ours bypassed the classical approach of constructing a probability measure from the inverse of the Kasteleyn matrix, but with the cost of no direct access to the fluctuation of height function in the liquid regions. The second project is an ongoing project with David Keating. We study a recently discovered structure known as perfect t-embedding on the complex plane, which would resolve the limitation of the previous project approach and complete the analysis of the Gaussian fluctuation of the height function in the liquid region of the dimer model. The existence of such planar embedding structures for dimer models implies that the fluctuations of the height function are governed by the Gaussian Free Field, which is a conjecture by Kenyon and Okounkov in 2007."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Dimer models and limit shapes from different perspectives"]}]}],"canonical_facts":{"dc:contributor":["Di Francesco, Philippe","Kedem, Rinat","Yong, Alexander","Russkikh, Marianna"],"dc:creator":["Vu, Hieu Trung"],"dc:date":["2025-05-01","2025-05"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms","The student, Hieu Trung Vu, accepted the attached license on 2025-04-23 at 19:43.","The student, Hieu Trung Vu, submitted this Dissertation for approval on 2025-04-23 at 19:50.","This Dissertation was approved for publication on 2025-05-01 at 08:49.","DSpace SAF Submission Ingestion Package generated from Vireo submission #21933 on 2025-10-19 at 18:18:55","This thesis considers two projects and some progress toward the theory of dimer models in statistical mechanics. The two questions we are trying to answer are the limit shapes of the dimer model and the height function fluctuation in the scaling limit. The first project considers the asymptotic and arctic curves of dimer models arising from a special set of initial data of the octahedron recurrence. This is a joint work with Di Francesco. This approach of ours bypassed the classical approach of constructing a probability measure from the inverse of the Kasteleyn matrix, but with the cost of no direct access to the fluctuation of height function in the liquid regions. The second project is an ongoing project with David Keating. We study a recently discovered structure known as perfect t-embedding on the complex plane, which would resolve the limitation of the previous project approach and complete the analysis of the Gaussian fluctuation of the height function in the liquid region of the dimer model. The existence of such planar embedding structures for dimer models implies that the fluctuations of the height function are governed by the Gaussian Free Field, which is a conjecture by Kenyon and Okounkov in 2007."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/129438"],"dc:language":["en","eng"],"dc:rights":["Copyright 2025 Hieu Trung Vu"],"dc:subject":["Dimer models","limit shapes","arctic curves","statistical mechanics","discrete complex analysis"],"dc:title":["Dimer models and limit shapes from different perspectives"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:05Z"}