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

8 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 - Jan 1 2014

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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