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The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates
Інший ID:
2010 Mathematics Subject Classification: 82B23; 82C22; 60J35
DOI:10.3842/SIGMA.2016.037
DOI:10.3842/SIGMA.2016.037
Посилання:
The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates / D. Wang, D. Waugh // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 19 назв. — англ.
Підтримка:
This paper is a 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 full collection is available at http://www.emis.de/journals/SIGMA/Deift-Tracy.html.
s
The authors are indebted to Ivan Corwin for numerous comments, especially on the relation to
the spectral theory and on the proof of Corollary 1.3. We also thank Eunghyun Lee for valuable
suggestions and comments. At last, we thank the anonymous referees for their comments,
suggestions and corrections, especially on a sign error in the manuscript. The first named
author is supported partially by the startup grant R-146-000-164-133.
Дата:
2016
Переглядів:
447
Завантажень:
202
Анотація:
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 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.
