The transition probability and the probability for the left-most particle's position of the q-totally asymmetric zero range process

Marko Korhonen, Eunghyun Lee

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We treat the N-particle zero range process whose jumping rates satisfy a certain condition. This condition is required to use the Bethe ansatz and the resulting model is the q-boson model by Sasamoto and Wadati ["Exact results for one-dimensional totally asymmetric diffusion models," J. Phys. A 31, 6057-6071 (1998)] or the qtotally asymmetric zero range process (TAZRP) by Borodin and Corwin ["Macdonald processes," Probab. Theory Relat. Fields (to be published)]. We find the explicit formula of the transition probability of the q-TAZRP via the Bethe ansatz. By using the transition probability we find the probability distribution of the left-most particle's position at time t. To find the probability for the left-most particle's position we find a newidentity corresponding to identity for the asymmetric simple exclusion process by Tracy andWidom ["Integral formulas for the asymmetric simple exclusion process," Commun. Math. Phys. 279, 815-844 (2008)]. For the initial state that all particles occupy a single site, the probability distribution of the left-most particle's position at time t is represented by the contour integral of a determinant.

Original languageEnglish
Article number013301
JournalJournal of Mathematical Physics
Volume55
Issue number1
DOIs
Publication statusPublished - 2014
Externally publishedYes

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Zero-range Process
Transition Probability
transition probabilities
Asymmetric Simple Exclusion Process
Bethe Ansatz
exclusion
Probability Distribution
Contour integral
Integral Formula
Diffusion Model
Exact Results
determinants
Bosons
Explicit Formula
Determinant
bosons
Model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

The transition probability and the probability for the left-most particle's position of the q-totally asymmetric zero range process. / Korhonen, Marko; Lee, Eunghyun.

In: Journal of Mathematical Physics, Vol. 55, No. 1, 013301, 2014.

Research output: Contribution to journalArticle

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