Geodesic
The Transition Probability of the $q$-TAZRP ($q$-Bosons) with Inhomogeneous Jump Rates
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{SIGMA_2016_12_a36,
     author = {Dong Wang and David Waugh},
     title = {The {Transition} {Probability} of the $q${-TAZRP} ($q${-Bosons)} with {Inhomogeneous} {Jump} {Rates}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2016},
     volume = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a36/}
}
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Dong Wang; David Waugh. The Transition Probability of the $q$-TAZRP ($q$-Bosons) with Inhomogeneous Jump Rates. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a36/

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