Related papers: Exact solution of the zero-range process: fundamen…
We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties…
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…
The slow-to-start mechanism is known to play an important role in the particular shape of the Fundamental diagram of traffic and to be associated to hysteresis effects of traffic flow.We study this question in the context of exclusion and…
In these lectures, we shall present some remarkable results that have been obtained for systems far from equilibrium during the last two decades. We shall put a special emphasis on the concept of large deviation functions that provide us…
As a simple model for single-file diffusion of hard core particles we investigate the one-dimensional symmetric exclusion process. We consider an open semi-infinite system where one end is coupled to an external reservoir of constant…
By an extension of the Bethe ansatz method used by Gwa and Spohn, we obtain an exact expression for the large deviation function of the time averaged current for the fully asymmetric exclusion process in a ring containing $N$ sites and $p$…
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between…
We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (1975) has shown that the long term behaviour of this process has a phase transition: If the particle production…
We present an exact solution for an asymmetric exclusion process on a ring with three classes of particles and vacancies. Using a matrix product Ansatz, we find explicit expressions for the weights of the configurations in the stationary…
Exact density profiles in the steady state of the one-dimensional fully asymmetric simple exclusion process on semi-infinite chains are obtained in the case of forward-ordered sequential dynamics by taking the thermodynamic limit in our…
We consider the totally asymmetric exclusion process in discrete time with generalized updating rules. We introduce a control parameter into the interaction between particles. Two particular values of the parameter correspond to known…
An asymmetric stochastic process describing the avalanche dynamics on a ring is proposed. A general kinetic equation which incorporates the exclusion and avalanche processes is considered. The Bethe ansatz method is used to calculate the…
We extend the circle theorem on the zeros of the partition function to a continuum system. We also calculate the exact zeros of the partition function for a finite system where the probability distribution for the order parameter is given…
Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…
A generalized zero-range process with a limited number of long-range interactions is studied as an example of a transport process in which particles at a T-junction make a choice of which branch to take based on traffic levels on each…
The zero-range process is a stochastic interacting particle system that exhibits a condensation transition under certain conditions on the dynamics. It has recently been found that a small perturbation of a generic class of jump rates leads…
We discuss the long-time limit of the integrated current distribution for the one-dimensional zero-range process with open boundaries. We observe that the current fluctuations become site-dependent above some critical current and argue that…
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 propose a new approach to perform numerical simulations of theta-vacuum like systems, test it in two analytically solvable models, and apply it to CP^3. The main new ingredient in our approach is the method used to compute the…
Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains with particles interacting with hard-core exclusion and moving along the channels and between them, are considered. In the limit of strong…