Related papers: Toric tableaux and the inhomogeneous two-species T…
We study a generalized two-species model on a ring. The original model [1] describes ordinary particles hopping exclusively in one direction in the presence of an impurity. The impurity hops with a rate different from that of ordinary…
The multispecies asymmetric simple exclusion process (mASEP) is a Markov chain in which particles of different species hop along a one-dimensional lattice. This paper studies the doubly asymmetric simple exclusion process…
Much of dynamical algebraic combinatorics focuses on global dynamical systems defined via maps that are compositions of local toggle operators. The second author and Roby studied such maps that result from toggling independent sets of a…
We define an algorithm on fermionic and bosonic twisted multiline queues that projects to the multispecies totally asymmetric simple exclusion process (TASEP) and the totally asymmetric zero range process (TAZRP) on a ring, respectively.…
We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class particles. Using the Bethe ansatz we present an…
For an arbitrary field K, let I be an ideal in the ring K[[x,y]] expressible as a polynomial in either the pair of ideals (x, y^4) and (x,y) or the pair (x,y^3) and (x^2, y). Let G be the group of automorphisms of K[[x,y]] sending the ideal…
In this paper, we study tree--like tableaux and some of their probabilistic properties. Tree--like tableaux are in bijection with other combinatorial structures, including permutation tableaux, and have a connection to the partially…
Recently James Martin introduced multiline queues, and used them to give a combinatorial formula for the stationary distribution of the multispecies asymmetric simple exclusion exclusion process (ASEP) on a circle. The ASEP is a model of…
The totally asymmetric simple exclusion process (TASEP) is a stochastic model for the unidirectional flow of interacting particles on a 1D-lattice that is much used in systems biology and statistical physics. Its master equation describes…
Type-B permutation tableaux are combinatorial objects introduced by Lam and Williams that have an interesting connection with the partially asymmetric simple exclusion process (PASEP). In this paper, we compute the expected value of several…
Ayyer and Linusson studied correlations in the multispecies TASEP on a ring (Trans AMS, 2017) using a combinatorial analysis of the multiline queues construction defined by Ferrari and Martin (AOP, 2008). It is natural to explore whether an…
In this paper we give a toric representation of the associated ring of a polyomino which is obtained by removing a convex polyomino from its ambient rectangle.
We study the non-equilibrium steady states in a totally-asymmetric simple-exclusion process with periodic boundary conditions, also incorporating (i) an extra (nearest-neighbour) repulsive interaction and (ii) hopping rates characterized by…
We introduce an $n$-species totally asymmetric zero range process ($n$-TAZRP) on one-dimensional periodic lattice with $L$ sites. It is a continuous time Markov process in which $n$ species of particles hop to the adjacent site only in one…
Consider the following Markov chain on permutations of length $n$. At each time step we choose a random position. If the letter at that position is smaller than the letter immediately to the left (cyclically) then these letters swap…
We study an $n$-species $t$-PushTASEP, an integrable long-range stochastic process, on a one-dimensional periodic lattice with inhomogeneities $x_1,\ldots,x_L$ and arbitrary capacity $l$ at each lattice site. The Markov matrix is identified…
A hypertoric variety is a quaternionic analogue of a toric variety. Just as the topology of toric varieties is closely related to the combinatorics of polytopes, the topology of hypertoric varieties interacts richly with the combinatorics…
We consider the set of forms of a toric variety over an arbitrary field: those varieties which become isomorphic to a toric variety after base field extension. In contrast to most previous work, we also consider arbitrary isomorphisms…
We discuss the approximate phenomenological description of the motion of a single second-class particle in a two-species totally asymmetric simple exclusion process (TASEP) on a 1D lattice. Initially, the second class particle is located at…
We examine the behavior of a single impurity particle embedded within a Totally Asymmetric Simple Exclusion Process (TASEP). By analyzing the impurity's dynamics, characterized by two arbitrary hopping parameters $ \alpha $ and $\beta$, we…