Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 037, 16 pages      arXiv:1512.01612
Contribution to the Special Issue on Asymptotics and Universality in Random Matrices, Random Growth Processes, Integrable Systems and Statistical Physics in honor of Percy Deift and Craig Tracy

The Transition Probability of the $q$-TAZRP ($q$-Bosons) with Inhomogeneous Jump Rates

Dong Wang a and David Waugh b
a) Department of Mathematics, National University of Singapore, 119076, Singapore
b) BNP Paribas, 787 7th Avenue, New York, NY, 10019, USA

Received January 03, 2016, in final form April 08, 2016; Published online April 14, 2016

In this paper we consider the $q$-deformed totally asymmetric zero range process ($q$-TAZRP), also known as the $q$-boson (stochastic) particle system, on the ${\mathbb Z}$ lattice, such that the jump rate of a particle depends on the site where it is on the lattice. We derive the transition probability for an $n$ particle process in Bethe ansatz form as a sum of $n!$ $n$-fold contour integrals. Our result generalizes the transition probability formula by Korhonen and Lee for $q$-TAZRP with a homogeneous lattice, and our method follows the same approach as theirs.

Key words: zero range process; transition probability; interacting particle systems; Bethe ansatz.

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