| 1. |
- Aas, E., et al.
(författare)
-
The exact phase diagram for a semipermeable TASEP with nonlocal boundary jumps
- 2019
-
Ingår i: Journal of Physics A. - : Institute of Physics Publishing (IOPP). - 1751-8113 .- 1751-8121. ; 52:35
-
Tidskriftsartikel (refereegranskat)abstract
- We consider a finite one-dimensional totally asymmetric simple exclusion process with four types of particles, {1, 0, 1, }, in contact with reservoirs. Particles of species 0 can neither enter nor exit the lattice, and those of species are constrained to lie at the first and last site. Particles of species 1 enter from the left reservoir into either the first or second site, move rightwards, and leave from either the last or penultimate site. Conversely, particles of species 1 enter from the right reservoir into either the last or penultimate site, move leftwards, and leave from either the first or last site. This dynamics is motivated by a natural random walk on the Weyl group of type D. We compute the exact nonequilibrium steady state distribution using a matrix ansatz building on earlier work of Arita. We then give explicit formulas for the nonequilibrium partition function as well as densities and currents of all species in the steady state, and derive the phase diagram.
|
|
| 2. |
- Alexandersson, Per, et al.
(författare)
-
The cyclic sieving phenomenon on circular Dyck paths
- 2019
-
Ingår i: The Electronic Journal of Combinatorics. - : ELECTRONIC JOURNAL OF COMBINATORICS. - 1097-1440 .- 1077-8926. ; 26:4
-
Tidskriftsartikel (refereegranskat)abstract
- We give a q-enumeration of circular Dyck paths, which is a superset of the classical Dyck paths enumerated by the Catalan numbers. These objects have recently been studied by Alexandersson and Panova. Furthermore, we show that this q-analogue exhibits the cyclic sieving phenomenon under a natural action of the cyclic group. The enumeration and cyclic sieving is generalized to Mobius paths. We also discuss properties of a generalization of cyclic sieving, which we call subset cyclic sieving, and introduce the notion of Lyndon-like cyclic sieving that concerns special recursive properties of combinatorial objects exhibiting the cyclic sieving phenomenon.
|
|
