### Abstract

In this paper we treat the multiparticle hopping asymmetric diffusion model (MADM) on ℤ introduced by Sasamoto and Wadati in 1998. The transition probability of the MADM with N particles is provided by using the Bethe ansatz. The transition probability is expressed as the sum of N-dimensional contour integrals of which contours are circles centered at the origin with restrictions on their radii. By using the transition probability we find ℙ(x _{m}(t)=x), the probability that the mth particle from the left is at x at time t. The probability ℙ(x _{m}(t)=x) is expressed as the sum of {pipe}S{pipe}-dimensional contour integrals over all S⊂{1,...,N} with {pipe}S{pipe}≥m, and is used to give the current distribution of the system. The mapping between the MADM and the pushing asymmetric simple exclusion process (PushASEP) is discussed.

Original language | English |
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Pages (from-to) | 50-72 |

Number of pages | 23 |

Journal | Journal of Statistical Physics |

Volume | 149 |

Issue number | 1 |

DOIs | |

Publication status | Published - Sep 7 2012 |

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### Keywords

- ASEP
- Bethe ansatz
- KPZ universality
- TASEP
- Tracy-Widom distribution

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics