Multivariate Eulerian polynomials and exclusion processes

Abstract

We give a new combinatorial interpretation of the stationary distribution of the (partially) asymmetric exclusion process on a finite number of sites in terms of decorated alternative trees and colored permutations. The corresponding expressions of the multivariate partition functions are then related to multivariate generalizations of Eulerian polynomials for colored permutations considered recently by N. Williams and the third author, and others. We also discuss stability-- and negative dependence properties satisfied by the partition functions.

13 pages (removed Conjecture 5.8 and updated references)

References in corpus (5)

• Homogeneous multivariate polynomials with the half-plane property
• The Lee-Yang and Pólya-Schur Programs. I. Linear Operators Preserving Stability
• Context-free Grammars and Multivariate Stable Polynomials over Stirling Permutations
• Stable multivariate $W$-Eulerian polynomials
• Weighted random staircase tableaux