Continued Fractions and the Partially Asymmetric Exclusion Process

Details Continued Fractions and the Partially Asymmetric Exclusion Process Continued Fractions and the Partially Asymmetric Exclusion Process

2009-04-25

arxiv.org/abs/0904.3947v1

J. Phys. A: Math. Theor. 42 325002 (2009)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1088/1751-8113/42/32/325002

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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