相关论文: Tableaux combinatorics of the two-species PASEP
We show that the known matrix representations of the stationary state algebra of the Asymmetric Simple Exclusion Process (ASEP) can be interpreted combinatorially as various weighted lattice paths. This interpretation enables us to use the…
The hopping motion of classical particles on a chain coupled to reservoirs at both ends is studied for parallel dynamics with arbitrary probabilities. The stationary state is obtained in the form of an alternating matrix product. The…
We study equilibrium properties of binary lattice-gases comprising $A$ and $B$ particles, which undergo continuous exchanges with their respective reservoirs, maintained at chemical potentials $\mu_A = \mu_B = \mu$. The particles interact…
2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level…
Zonotopes are a rich and fascinating family of polytopes, with connections to many areas of mathematics. In this article we provide a brief survey of classical and recent results related to lattice zonotopes. Our emphasis is on connections…
The object of the present article is a 1d lattice-gas system comprised of soft-particles, wherein particles interact only if they occupy the same or a neighboring site, as a simple representation of penetrable particles of soft condensed…
We introduce and study a simple and natural class of solvable stochastic lattice gases. This is the class of \emph{Strong Particles}. The name is due to the fact that when they try to jump to an occupied site they succeed pushing away a…
We study a minimal lattice model which describes bidirectional transport of "particles" driven along a one dimensional track, as is observed in microtubule based, motor protein driven bidirectional transport of cargo vesicles, lipid bodies…
The lattice of flats $\mathcal L_M$ of a matroid $M$ is combinatorially well-behaved and, when $M$ is realizable, admits a geometric model in the form of a "Schubert variety of hyperplane arrangement". In contrast, the lattice of flats of a…
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…
This paper introduces a multi-species version of a process called ASEP(q,j). In this process, up to 2j particles are allowed to occupy a lattice site, the particles drift to the right with asymmetry 0<q^{2j}<1, and there are n-1 species of…
Several theoretical models based on totally asymmetric simple exclusion process (TASEP) have been extensively utilized to study various non-equilibrium transport phenomena. Inspired by the the role of microtubule-transported vesicles in…
An ASEP with two species of particles and different hopping rates is considered on a ring. Its integrability is proved and the Nested Algebraic Bethe Ansatz is used to derive the Bethe Equations for states with arbitrary numbers of…
In combinatorics there is a well-known duality between non-nesting and non-crossing objects. In algebra there are many objects which are standard, for example Standard Young Tableaux, Standard Monomials, Standard Bitableaux. We adopt a…
Let us consider a two-sided multi-species stochastic particle model with finitely many particles on $\mathbb{Z}$ defined as follows. Suppose that each particle is labelled by a positive integer $l$ and waits a random time exponentially…
We consider a finite one-dimensional totally asymmetric simple exclusion process (TASEP) with four types of particles, $\{1,0,\bar{1},*\}$, in contact with reservoirs. Particles of species $0$ can neither enter nor exit the lattice, and…
In this paper, we introduce an ASEP-like transport model for bidirectional motion of particles on a multi-lane lattice. The model is motivated by {\em in vivo} experiments on organelle motility along a microtubule (MT), consisting of…
A system consisting of two parallel coupled channels where particles in one of them follow the rules of totally asymmetric exclusion processes (TASEP) and in another one move as in symmetric simple exclusion processes (SSEP) is investigated…
Active motion of molecules along filamentous structures is a crucial feature of cell biology and is often modeled with the paradigmatic asymmetric simple exclusion process. Motivated by recent experimental studies that have addressed the…
In this paper, we study tree--like tableaux, combinatorial objects which exhibit a natural tree structure and are connected to the partially asymmetric simple exclusion process (PASEP). There was a conjecture made on the total number of…