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Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and…
The asymmetric simple exclusion process (ASEP) is a paradigmatic driven-diffusive system that describes the asymmetric diffusion of particles with hardcore interactions in a lattice. Although the ASEP is known as an exactly solvable model,…
We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…
We propose and study a one-dimensional (1D) model consisting of two lanes with open boundaries. One of the lanes executes diffusive and the other lane driven unidirectional or asymmetric exclusion dynamics, which are mutually coupled…
This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks in the quarter plane are characterized by the fact that the one-step transition probabilities…
We consider steady-state current activity statistics for the one-dimensional totally asymmetric simple exclusion process (TASEP). With the help of the known operator algebra (for general open boundary conditions), as well as general…
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 study the steady-state behavior of a driven non-equilibrium lattice gas of hard-core particles with next-nearest-neighbor interaction. We calculate the exact stationary distribution of the periodic system and for a particular line in the…
We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…
We consider the totally asymmetric simple exclusion process (TASEP) on the periodic chain in the presence of a single impurity site that is inaccessible to other particles and therefore acts as a static defect. Particles are allowed to…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
This article introduces a model for interacting vertex-reinforced random walks, each taking values on a complete sub-graph of a locally finite undirected graph. The transition probability for a walk to a given vertex depends on the…
The asymmetric simple exclusion process (ASEP) with periodic boundary conditions is investigated for shuffled dynamics. In this type of update, in each discrete timestep the particles are updated in a random sequence. Such an update is…
We study a one-dimensional anisotropic exclusion process describing particles injected at the origin, moving to the right on a chain of $L$ sites and being removed at the (right) boundary. We construct the steady state and compute the…
We study symmetric simple exclusion processes (SSEP) on a ring in the presence of uniformly moving multiple defects or disorders - a generalization of the model proposed earlier [Phys. Rev. E 89, 022138 (2014)]. The defects move with…
Considering the large deviations of activity and current in the Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between the joint scaled cumulant generating functions of activity and…
An asymmetric exclusion model on an open chain with random rates for hopping particles, where overtaking is also possible, is studied numerically and by computer simulation. The phase structure of the model and the density profiles near the…
The asymmetric simple exclusion process (ASEP) is a model of particle transport used in the study of biological processes such as mRNA translation. In 2014, Zhao and Krishnan introduced a new approach for analyzing the ASEP using…
In this paper it is shown that the steady-state weights of the asymmetric simple exclusion process (ASEP) with open boundaries and parallel update can be written as a product of a scalar pair-factorized and a matrix-product state. This type…
We consider the asymmetric exclusion process (ASEP) in one dimension on sites $i = 1,..., N$, in contact at sites $i=1$ and $i=N$ with infinite particle reservoirs at densities $\rho_a$ and $\rho_b$. As $\rho_a$ and $\rho_b$ are varied, the…