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This article is cited in 9 scientific papers (total in 9 papers)
The Transition Probability of the $q$-TAZRP ($q$-Bosons) with Inhomogeneous Jump Rates
Dong Wanga, David Waughb a Department of Mathematics, National University of Singapore, 119076, Singapore
b BNP Paribas, 787 7th Avenue, New York, NY, 10019, USA
Abstract:
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.
Keywords:
zero range process; transition probability; interacting particle systems; Bethe ansatz.
Received: January 3, 2016; in final form April 8, 2016; Published online April 14, 2016
Citation:
Dong Wang, David Waugh, “The Transition Probability of the $q$-TAZRP ($q$-Bosons) with Inhomogeneous Jump Rates”, SIGMA, 12 (2016), 037, 16 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1119 https://www.mathnet.ru/eng/sigma/v12/p37
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Abstract page: | 113 | Full-text PDF : | 36 | References: | 34 |
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