Related papers: The inhomogeneous $t$-PushTASEP and Macdonald poly…
We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with…
We present the transition probability for the asymmetric simple exclusion process on the half-space for general initial conditions and particle insertion at the boundary. In the limit of total asymmetry, where particles only jump to the…
We focus on the probability distribution function (pdf) $P(\Delta \gamma; \gamma)$ where $\Delta \gamma$ are the {\em measured} strain intervals between plastic events in an athermal strained amorphous solids, and $\gamma$ measures the…
We study the flux of totally asymmetric simple exclusion processes (TASEPs) on a twin co-axial square tracks. In this biologically motivated model the particles in each track act as mobile bottlenecks against the movement of the particles…
We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent…
We explore the stationary densities in totally asymmetric exclusion processes (TASEP) with open boundary conditions and spatially inhomogeneous hopping rates. We calculate the steady state density profiles that characterise the associated…
We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…
Consider an inhomogeneous multi-species TASEP with drift to the left, and define a height function which equals the maximum species number to the left of a lattice site. For each fixed time, the multi-point distributions of these height…
The totally asymmetric simple exclusion process (TASEP) is a paradigmatic lattice model for one-dimensional particle transport subject to excluded-volume interactions. Solving the inhomogeneous TASEP in which particles' hopping rates vary…
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…
Macdonald superpolynomials provide a remarkably rich generalization of the usual Macdonald polynomials. The starting point of this work is the observation of a previously unnoticed stability property of the Macdonald superpolynomials when…
We consider invariant transports of stationary random measures on $\mathbb{R}^d$ and establish natural mixing criteria that guarantee persistence of asymptotic variances. To check our mixing assumptions, which are based on two-point Palm…
We study the steady state of the two-species Asymmetric Simple Exclusion Process (ASEP) with open boundary conditions. The matrix product method works for the determination of the stationary probability distribution. Several physical…
A multi-species generalization of the asymmetric simple exclusion process (ASEP) is studied in ordered sequential and sub-lattice parallel updating schemes. In this model particles hop with their own specific probabilities to their…
Theoretical advances in the study of non-equilibrium phenomena are briefly reviewed with emphasis on steady state properties of one-dimensional driven lattice gases. The presentation is focused on the totally asymmetric simple-exclusion…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
By generalizing the algebra of operators of the Asymmetric Simple Exclusion Process (ASEP), a multi-species ASEP in which particles can overtake each other,is defined on both open and closed one dimensional chains. On the ring the steady…
In this work, we show a connection between superstatistics and position-dependent mass (PDM) systems in the context of the canonical ensemble. The key point is to set the fluctuation distribution of the inverse temperature in terms od the…
The purpose of this work is to build a framework that allows for an in-depth study of various generalisations to inhomogeneous space of models of Borodin-Ferrari, Dieker-Warren, Nordenstam, Warren-Windridge of interacting particles in…
We revisit the problem of constructing the stationary states of the multispecies asymmetric simple exclusion process on a one-dimensional periodic lattice. Central to our approach is a quantum oscillator weighted five vertex model which…