A combinatorial derivation of the PASEP stationary state
The electronic journal of combinatorics, Tome 13 (2006)
We give a combinatorial derivation and interpretation of the weights associated with the stationary distribution of the partially asymmetric exclusion process. We define a set of weight equations, which the stationary distribution satisfies. These allow us to find explicit expressions for the stationary distribution and normalisation using both recurrences and path models. To show that the stationary distribution satisfies the weight equations, we construct a Markov chain on a larger set of generalised configurations. A bijection on this new set of configurations allows us to find the stationary distribution of the new chain. We then show that a subset of the generalised configurations is equivalent to the original process and that the stationary distribution on this subset is simply related to that of the original chain. We also provide a direct proof of the validity of the weight equations.
@article{10_37236_1134,
author = {Richard Brak and Sylvie Corteel and John Essam and Robert Parviainen and Andrew Rechnitzer},
title = {A combinatorial derivation of the {PASEP} stationary state},
journal = {The electronic journal of combinatorics},
year = {2006},
volume = {13},
doi = {10.37236/1134},
zbl = {1110.60028},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1134/}
}
TY - JOUR AU - Richard Brak AU - Sylvie Corteel AU - John Essam AU - Robert Parviainen AU - Andrew Rechnitzer TI - A combinatorial derivation of the PASEP stationary state JO - The electronic journal of combinatorics PY - 2006 VL - 13 UR - http://geodesic.mathdoc.fr/articles/10.37236/1134/ DO - 10.37236/1134 ID - 10_37236_1134 ER -
%0 Journal Article %A Richard Brak %A Sylvie Corteel %A John Essam %A Robert Parviainen %A Andrew Rechnitzer %T A combinatorial derivation of the PASEP stationary state %J The electronic journal of combinatorics %D 2006 %V 13 %U http://geodesic.mathdoc.fr/articles/10.37236/1134/ %R 10.37236/1134 %F 10_37236_1134
Richard Brak; Sylvie Corteel; John Essam; Robert Parviainen; Andrew Rechnitzer. A combinatorial derivation of the PASEP stationary state. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1134
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