Continued Fractions and the Partially Asymmetric Exclusion Process

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 normalisation 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.

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Cited by in corpus (10)

• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Combinatorial mappings of exclusion processes
• Stationary measures of the KPZ equation on an interval from Enaud-Derrida's matrix product ansatz representation
• Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
• KPZ fluctuations in finite volume
• Bose-Einstein condensation and a two-dimensional walk model
• Fluctuations of random Motzkin paths
• The parallel TASEP, fixed particle number and weighted Motzkin paths
• A heterogeneous zero-range process related to a two-dimensional walk model
• Thermal resonating Hartree-Bogoliubov theory based on the projection method