{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/132551"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/132551","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Probabilistic techniques for large-scale coordination and clustering","abstract":"This is a study of probabilistic methods used in coordination and clustering problems that arise in operations research. Specifically, we focus on infinite graph and infinite point process methods to analyze the dynamics of blockchains, the Hegselmann--Krause model, and a stochastic dynamic clustering model for data science. For blockchains, we show that the $t \\to \\infty$ limit is crucial for understanding how and when consensus occurs. Specifically, we use a randomly delayed recursion to capture the network dynamics, and show that in this model, an asymptotic criterion called one-endedness of the limiting blockchain is crucial to achieving consensus. We then study the distribution of the time to consensus. For the Hegselmann--Krause and dynamic clustering models, we show how stationarity and other symmetries of point processes shed insights into the nature of the fixed points. Included here is a formal statement and partial resolution of the $2R$-Conjecture for the Hegselmann--Krause model, which has been open (without a formal statement) since 2007. Our dynamic clustering model is also new and directly addresses the problem on an infinite dataset, rather than treating it as a limit of pre-limiting finite datasets. We show that this model has a unique stationary measure, with strong implications for the question of when to accept the clusters produced by a dynamic clustering algorithm.","abstract_html":"This is a study of probabilistic methods used in coordination and clustering problems that arise in operations research. Specifically, we focus on infinite graph and infinite point process methods to analyze the dynamics of blockchains, the Hegselmann--Krause model, and a stochastic dynamic clustering model for data science. For blockchains, we show that the $t \\to \\infty$ limit is crucial for understanding how and when consensus occurs. Specifically, we use a randomly delayed recursion to capture the network dynamics, and show that in this model, an asymptotic criterion called one-endedness of the limiting blockchain is crucial to achieving consensus. We then study the distribution of the time to consensus. For the Hegselmann--Krause and dynamic clustering models, we show how stationarity and other symmetries of point processes shed insights into the nature of the fixed points. Included here is a formal statement and partial resolution of the $2R$-Conjecture for the Hegselmann--Krause model, which has been open (without a formal statement) since 2007. Our dynamic clustering model is also new and directly addresses the problem on an infinite dataset, rather than treating it as a limit of pre-limiting finite datasets. We show that this model has a unique stationary measure, with strong implications for the question of when to accept the clusters produced by a dynamic clustering algorithm.","abstract_has_math":true,"creators":["Gopalan, Aditya S."],"institution":"University of Illinois Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Industrial Engineering","degree_department":null,"school":null,"contributors":["Dey, Partha S","Etesami, S. Rasoul","Sowers, Richard B","Subramanian, Vijay G"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-12","date_published":"2025-12","updated_at":"2026-07-22T22:25:07Z","subjects":["Blockchain","Hegselmann--Krause","Clustering","Distributed Averaging","Consensus"],"languages":["en"],"rights":["Copyright 2025 Aditya Gopalan"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/132551","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dey, Partha S","Etesami, S. 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Specifically, we focus on infinite graph and infinite point process methods to analyze the dynamics of blockchains, the Hegselmann--Krause model, and a stochastic dynamic clustering model for data science. For blockchains, we show that the $t \\to \\infty$ limit is crucial for understanding how and when consensus occurs. Specifically, we use a randomly delayed recursion to capture the network dynamics, and show that in this model, an asymptotic criterion called one-endedness of the limiting blockchain is crucial to achieving consensus. We then study the distribution of the time to consensus. For the Hegselmann--Krause and dynamic clustering models, we show how stationarity and other symmetries of point processes shed insights into the nature of the fixed points. Included here is a formal statement and partial resolution of the $2R$-Conjecture for the Hegselmann--Krause model, which has been open (without a formal statement) since 2007. Our dynamic clustering model is also new and directly addresses the problem on an infinite dataset, rather than treating it as a limit of pre-limiting finite datasets. We show that this model has a unique stationary measure, with strong implications for the question of when to accept the clusters produced by a dynamic clustering algorithm.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2026-02-19 without embargo terms","The student, Aditya Gopalan, accepted the attached license on 2025-12-01 at 11:05.","The student, Aditya Gopalan, submitted this Dissertation for approval on 2025-12-01 at 11:08.","This Dissertation was approved for publication on 2025-12-01 at 16:41.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22993 on 2026-02-19 at 18:25:55"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Probabilistic techniques for large-scale coordination and clustering"]}]}],"canonical_facts":{"dc:contributor":["Dey, Partha S","Etesami, S. Rasoul","Sowers, Richard B","Subramanian, Vijay G"],"dc:creator":["Gopalan, Aditya S."],"dc:date":["2025-12","2025-12-01"],"dc:description":["This is a study of probabilistic methods used in coordination and clustering problems that arise in operations research. Specifically, we focus on infinite graph and infinite point process methods to analyze the dynamics of blockchains, the Hegselmann--Krause model, and a stochastic dynamic clustering model for data science. For blockchains, we show that the $t \\to \\infty$ limit is crucial for understanding how and when consensus occurs. Specifically, we use a randomly delayed recursion to capture the network dynamics, and show that in this model, an asymptotic criterion called one-endedness of the limiting blockchain is crucial to achieving consensus. We then study the distribution of the time to consensus. For the Hegselmann--Krause and dynamic clustering models, we show how stationarity and other symmetries of point processes shed insights into the nature of the fixed points. Included here is a formal statement and partial resolution of the $2R$-Conjecture for the Hegselmann--Krause model, which has been open (without a formal statement) since 2007. Our dynamic clustering model is also new and directly addresses the problem on an infinite dataset, rather than treating it as a limit of pre-limiting finite datasets. We show that this model has a unique stationary measure, with strong implications for the question of when to accept the clusters produced by a dynamic clustering algorithm.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2026-02-19 without embargo terms","The student, Aditya Gopalan, accepted the attached license on 2025-12-01 at 11:05.","The student, Aditya Gopalan, submitted this Dissertation for approval on 2025-12-01 at 11:08.","This Dissertation was approved for publication on 2025-12-01 at 16:41.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22993 on 2026-02-19 at 18:25:55"],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/132551"],"dc:language":["en"],"dc:rights":["Copyright 2025 Aditya Gopalan"],"dc:subject":["Blockchain","Hegselmann--Krause","Clustering","Distributed Averaging","Consensus"],"dc:title":["Probabilistic techniques for large-scale coordination and clustering"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Industrial Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:07Z"}