{"id":{"repo_id":"nus","oai_identifier":"oai:scholarbank.nus.edu.sg:10635/119494"},"canonical_url":"https://search.dev.ndltd.org/etd/nus/oai:scholarbank.nus.edu.sg:10635/119494","repository":{"repo_id":"nus","name":"National University of Singapore","base_url":"https://scholarbank.nus.edu.sg/oai/request"},"display":{"title":"The Transition Probability of the Inhomogeneous q-TAZRP","abstract":"In this thesis we study the transition probability of the q-TAZRP, a special form of the n-particle totally asymmetric zero-range process (TAZRP) on the lattice Z defined by Sasamoto and Wadati in [J. Phys. A, vol. 31 6057--6071 (1998)]. We generalise the result by Korhonen and Lee in [J. Math. Phys., vol. 55, 013301 (2014)] to allow the lattice sites to have different conductances, while in [K-L] they are identical. We use the Bethe ansatz to derive an integral formula for the transition probability for the n-particle system, which reduces to the formula in [K-L] if all the conductance parameters are identically 1. Our result is comparable to the result obtained by Borodin, Corwin and Sasamoto [Ann. Prob., vol. 42, no. 6, 2314-2382 (2014)] for q-TASEP model where particles have different jumping rates.","abstract_html":"In this thesis we study the transition probability of the q-TAZRP, a special form of the n-particle totally asymmetric zero-range process (TAZRP) on the lattice Z defined by Sasamoto and Wadati in [J. Phys. A, vol. 31 6057--6071 (1998)]. We generalise the result by Korhonen and Lee in [J. Math. Phys., vol. 55, 013301 (2014)] to allow the lattice sites to have different conductances, while in [K-L] they are identical. We use the Bethe ansatz to derive an integral formula for the transition probability for the n-particle system, which reduces to the formula in [K-L] if all the conductance parameters are identically 1. Our result is comparable to the result obtained by Borodin, Corwin and Sasamoto [Ann. Prob., vol. 42, no. 6, 2314-2382 (2014)] for q-TASEP model where particles have different jumping rates.","abstract_has_math":false,"creators":["DAVID WAUGH"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-16","date_published":"2015-01-16","updated_at":"2026-07-24T03:33:34Z","subjects":["TAZRP TASEP Tracy-Widom Bethe ansatz"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["DAVID WAUGH"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2015-01-16"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://scholarbank.nus.edu.sg/handle/10635/119494"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["TAZRP TASEP Tracy-Widom Bethe ansatz"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://scholarbank.nus.edu.sg/bitstreams/62205128-af7b-4054-8f06-8071f9b61578/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we study the transition probability of the q-TAZRP, a special form of the n-particle totally asymmetric zero-range process (TAZRP) on the lattice Z defined by Sasamoto and Wadati in [J. Phys. A, vol. 31 6057--6071 (1998)]. We generalise the result by Korhonen and Lee in [J. Math. Phys., vol. 55, 013301 (2014)] to allow the lattice sites to have different conductances, while in [K-L] they are identical. We use the Bethe ansatz to derive an integral formula for the transition probability for the n-particle system, which reduces to the formula in [K-L] if all the conductance parameters are identically 1. Our result is comparable to the result obtained by Borodin, Corwin and Sasamoto [Ann. Prob., vol. 42, no. 6, 2314-2382 (2014)] for q-TASEP model where particles have different jumping rates."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["e89d062fb523ef00561b714a391a7756","dfd56c1e4ccc39ab65ab59037f37187a"]},{"key":"dc:title","label":"Title","values":["The Transition Probability of the Inhomogeneous q-TAZRP"]}]}],"canonical_facts":{"dc:creator":["DAVID WAUGH"],"dc:date.issued":["2015-01-16"],"dc:description.abstract":["In this thesis we study the transition probability of the q-TAZRP, a special form of the n-particle totally asymmetric zero-range process (TAZRP) on the lattice Z defined by Sasamoto and Wadati in [J. Phys. A, vol. 31 6057--6071 (1998)]. We generalise the result by Korhonen and Lee in [J. Math. Phys., vol. 55, 013301 (2014)] to allow the lattice sites to have different conductances, while in [K-L] they are identical. We use the Bethe ansatz to derive an integral formula for the transition probability for the n-particle system, which reduces to the formula in [K-L] if all the conductance parameters are identically 1. Our result is comparable to the result obtained by Borodin, Corwin and Sasamoto [Ann. Prob., vol. 42, no. 6, 2314-2382 (2014)] for q-TASEP model where particles have different jumping rates."],"dc:format.checksum.md5":["e89d062fb523ef00561b714a391a7756","dfd56c1e4ccc39ab65ab59037f37187a"],"dc:identifier.uri":["https://scholarbank.nus.edu.sg/bitstreams/62205128-af7b-4054-8f06-8071f9b61578/download"],"dc:relation.isreferencedby":["https://scholarbank.nus.edu.sg/handle/10635/119494"],"dc:subject":["TAZRP TASEP Tracy-Widom Bethe ansatz"],"dc:title":["The Transition Probability of the Inhomogeneous q-TAZRP"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T03:33:34Z"}