Continued fractions and the partially asymmetric exclusion process

R. A. Blythe, W. Janke, D. A. Johnston, R. Kenna

Research output: Contribution to journalArticle

10 Citations (Scopus)

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 languageEnglish
Article number325002
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number32
DOIs
Publication statusPublished - 2009

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