Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/119494
Title: The Transition Probability of the Inhomogeneous q-TAZRP
Authors: DAVID WAUGH
Keywords: TAZRP TASEP Tracy-Widom Bethe ansatz
Issue Date: 16-Jan-2015
Source: DAVID WAUGH (2015-01-16). The Transition Probability of the Inhomogeneous q-TAZRP. ScholarBank@NUS Repository.
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.
URI: http://scholarbank.nus.edu.sg/handle/10635/119494
Appears in Collections:Master's Theses (Open)

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