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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 037, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.037
(Mi sigma1119)
 

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
Full-text PDF (434 kB) Citations (9)
References:
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.
Funding agency
The first named author is supported partially by the startup grant R-146-000-164-133.
Received: January 3, 2016; in final form April 8, 2016; Published online April 14, 2016
Bibliographic databases:
Document Type: Article
MSC: 82B23; 82C22; 60J35
Language: English
Citation: Dong Wang, David Waugh, “The Transition Probability of the $q$-TAZRP ($q$-Bosons) with Inhomogeneous Jump Rates”, SIGMA, 12 (2016), 037, 16 pp.
Citation in format AMSBIB
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\by Dong~Wang, David~Waugh
\paper The Transition Probability of the $q$-TAZRP ($q$-Bosons) with Inhomogeneous Jump Rates
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\yr 2016
\vol 12
\papernumber 037
\totalpages 16
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  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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