Name
Abstract | ||
|---|---|---|
The partially asymmetric exclusion process (PASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites. It is partially asymmetric in the sense that the probability of hopping left is q times the probability of hopping right. Additionally, particles may enter from the left with probability @a and exit from the right with probability @b. In this paper we prove a close connection between the PASEP and the combinatorics of permutation tableaux. (These tableaux come indirectly from the totally nonnegative part of the Grassmannian, via work of Postnikov, and were studied in a paper of Steingrimsson and the second author.) Namely, we prove that in the long time limit, the probability that the PASEP is in a particular configuration @t is essentially the generating function for permutation tableaux of shape @l(@t) enumerated according to three statistics. The proof of this result uses a result of Derrida, Evans, Hakim, and Pasquier on the matrix ansatz for the PASEP model. As an application, we prove some monotonicity results for the PASEP. We also derive some enumerative consequences for permutations enumerated according to various statistics such as weak excedence set, descent set, crossings, and occurrences of generalized patterns. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.aam.2006.08.002 | Advances in Applied Mathematics |
Keywords | Field | DocType |
monotonicity result,generalized patterns. 1,generalized pattern,important model,enumerative consequence,pasep model,tableaux combinatorics,matrix ansatz,weak excedence set,eulerian numbers,. permutation tableax,close connection,asymmetric exclusion process,permutation tableau,descent set,generating function,statistical mechanics | Generating function,Ansatz,Monotonic function,Discrete mathematics,Combinatorics,Statistical mechanics,Mathematical analysis,Matrix (mathematics),Permutation,Probability distribution,Grassmannian,Mathematics | Journal |
Volume | Issue | ISSN |
39 | 3 | 0196-8858 |
Citations | PageRank | References |
28 | 3.57 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sylvie Corteel | 1 | 266 | 36.33 |
| Lauren K. Williams | 2 | 78 | 9.16 |