## Abstract

We note that a tridiagonal matrix representation of the algebra of the partially asymmetric exclusion process (PASEP) lends itself to interpretation as the transfer matrix for weighted Motzkin lattice paths. A continued-fraction ('J fraction') representation of the lattice-path-generating function is particularly well suited to discussing the PASEP, for which the paths have height-dependent weights. We show that this not only allows a succinct derivation of the normalization and correlation lengths of the PASEP, but also reveals how finite-dimensional representations of the PASEP algebra, valid only along special lines in the phase diagram, relate to the general solution that requires an infinite-dimensional representation.

Original language | English |
---|---|

Article number | 325002 |

Pages (from-to) | - |

Number of pages | 21 |

Journal | Journal of physics a-Mathematical and theoretical |

Volume | 42 |

Issue number | 32 |

DOIs | |

Publication status | Published - 14 Aug 2009 |

## Keywords

- OPEN BOUNDARIES
- COMBINATORIAL APPROACH
- JUMPING PARTICLES
- MODEL
- POLYNOMIALS
- ALGEBRA
- STATES