相关论文: From duality to determinants for q-TASEP and ASEP
We study a new process, which we call ASEP$(q,j)$, where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by $q\in (0,1)$ and where at most $2j\in\mathbb{N}$ particles per site are allowed. The…
The one-dimensional totally asymmetric simple exclusion process (TASEP) with $N$ particles on a periodic lattice of $L$ sites is an interacting particle system with hopping rates breaking detailed balance. The total time-integrated current…
Two new interacting particle systems are introduced in this paper: dynamic versions of the asymmetric inclusion process (ASIP) and the asymmetric Brownian energy process (ABEP). Dualities and reversibility of these processes are proven,…
We consider from a microscopic perspective large deviation properties of several stochastic interacting particle systems, using their mapping to integrable quantum spin systems. A brief review of recent work is given and several new results…
We consider any fixed $d\in\mathbb{Z}_{>0}$ number of second class particles in the asymmetric simple exclusion process (ASEP), constructed via a basic coupling of two ASEPs. We give the joint distribution of the positions of the second…
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…
We study the joint exit probabilities of particles in the totally asymmetric simple exclusion process (TASEP) from space-time sets of given form. We extend previous results on the space-time correlation functions of the TASEP, which…
We study an interacting particle process on a finite ring with $L$ sites with at most $K$ particles per site, in which particles hop to nearest neighbors with rates given in terms of $t$-deformed integers and asymmetry parameter $q$, where…
In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum…
Many integrable stochastic particle systems in one space dimension (such as TASEP - totally asymmetric simple exclusion process - and its various deformations, with a notable exception of ASEP) remain integrable when we equip each particle…
We introduce a four-parameter family of interacting particle systems on the line which can be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which enjoy certain Markov dualities. Using this, for the systems…
We study the one dimensional partially asymmetric simple exclusion process (ASEP) with open boundaries, that describes a system of hard-core particles hopping stochastically on a chain coupled to reservoirs at both ends. Derrida, Evans,…
We investigate dual mechanisms for interacting particle systems. Generalizing an approach of Alkemper and Hutzenthaler in the case of coalescing duals, we show that a simple linear transformation leads to a moment duality of suitably…
We present two new connections between the inhomogeneous stochastic higher spin six vertex model in a quadrant and integrable stochastic systems from the Macdonald processes hierarchy. First, we show how Macdonald $q$-difference operators…
Exclusion processes in one dimension first appeared in the 70s and have since dragged much attention from communities in different domains: stochastic processes, out-of-equilibriums statistical physics, and more recently integrable systems.…
The asymmetric simple exclusion process (ASEP) is a paradigmatic nonequilibrium many-body system that describes the asymmetric random walk of particles with exclusion interactions in a lattice. Although the ASEP is recognized as an exactly…
We develop spectral theory for the q-Hahn stochastic particle system introduced recently by Povolotsky. That is, we establish a Plancherel type isomorphism result which implies completeness and biorthogonality statements for the Bethe…
Macdonald processes are probability measures on sequences of partitions defined in terms of nonnegative specializations of the Macdonald symmetric functions and two Macdonald parameters q,t in [0,1). We prove several results about these…
We study the nonextensive thermodynamics for open systems. On the basis of the maximum entropy principle, the dual power-law q-distribution functions are re-deduced by using the dual particle number definitions and assuming that the…
We reformulate the Corteel-Williams equations for the stationary state of the two parameter Asymmetric Simple Exclusion Process (TASEP) as a linear map $\mathcal{L}(\,\cdot\,)$, acting on a tensor algebra built from a rank two free module…