Related papers: The $q$-Hahn asymmetric exclusion process
We compute the one-point probability distribution for the stationary KPZ equation (i.e. initial data H(0,X)=B(X), for B(X) a two-sided standard Brownian motion) and show that as time T goes to infinity, the fluctuations of the height…
We explore probabilistic consequences of correspondences between $q$-Whittaker measures and periodic and free boundary Schur measures established by the authors in the recent paper [arXiv:2106.11922]. The result is a comprehensive theory of…
In this paper we treat the multiparticle hopping asymmetric diffusion model (MADM) of which initial configuration is such that a single site is occupied by infinitely many particles and all other sites are empty. We show that the…
We introduce the strict-weak polymer model, and show the KPZ universality of the free energy fluctuation of this model for a certain range of parameters. Our proof relies on the observation that the discrete time geometric q-TASEP model,…
We introduce the $q$-Hahn PushTASEP --- an integrable stochastic interacting particle system which is a 3-parameter generalization of the PushTASEP, a well-known close relative of the TASEP (Totally Asymmetric Simple Exclusion Process). The…
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 consider the one-dimensional partially asymmetric exclusion process with random hopping rates, in which a fraction of particles (or sites) have a preferential jumping direction against the global drift. In this case the accumulated…
In previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step initial condition, particles beginning at the positive integers. There it was shown that the probability distribution…
These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the…
The one-dimensional totally asymmetric simple exclusion process (TASEP), a Markov process describing classical hard-core particles hopping in the same direction, is considered on a periodic lattice of $L$ sites. The relaxation to the…
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 introduce two new exactly solvable (stochastic) interacting particle systems which are discrete time versions of q-TASEP. We call these geometric and Bernoulli discrete time q-TASEP. We obtain concise formulas for expectations of a large…
We study the one-dimensional discrete time totally asymmetric simple exclusion process with parallel update rules on a spatially periodic domain. A multi-point space-time joint distribution formula is obtained for general initial…
We obtain exact formulas for moments and generating functions of the height function of the asymmetric simple exclusion process at one spatial point, starting from special initial data in which every positive even site is initially…
We consider the q-TASEP that is a q-deformation of the totally asymmetric simple exclusion process (TASEP) on Z for q in [0,1) where the jump rates depend on the gap to the next particle. For step initial condition, we prove that the…
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…
For the two-sided Bernoulli initial condition with density $\rho_-$ (resp. $\rho_+$) to the left (resp. to the right), we study the distribution of a tagged particle in the one dimensional symmetric simple exclusion process. We obtain a…
We study the totally asymmetric simple exclusion process (TASEP) on $\mathbb{Z}$ with a general initial condition and a deterministically moving wall in front of the particles. Using colour-position symmetry, we express the one-point…
We consider the asymmetric simple exclusion process in one dimension with weak asymmetry (WASEP) and 0-1 step initial condition. Our interest are the fluctuations of the time-integrated particle current at some prescribed spatial location.…
We analyze a class of non-simple exclusion processes and the corresponding growth models by generalizing Gaertners Cole-Hopf transformation. We identify the main non-linearity and eliminate it by imposing a gradient type condition. For…