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.