### 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. © 2009 IOP Publishing Ltd.

Original language | English |
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Article number | 325002 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 32 |

DOIs | |

Publication status | Published - 2009 |

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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*42*(32), [325002]. https://doi.org/10.1088/1751-8113/42/32/325002