Related papers: Particle Ordering in Zero Range Process : Exact sp…
The phenomenon of phase transitions in one-dimensional systems is discussed. Equilibrium systems are reviewed and some properties of an energy function which may allow phase transitions and phase ordering in one dimension are identified. We…
We study an open-boundary version of the on-off zero-range process introduced in Hirschberg et al. [Phys. Rev. Lett. 103, 090602 (2009)]. This model includes temporal correlations which can promote the condensation of particles, a situation…
We give bounds on the rate of convergence to equilibrium of the symmetric simple exclusion process in $\Z^d$. Our results include the existent results in the literature. We get better bounds and larger class of initial states via a unified…
We study a model for microscopic segregation in a homogeneous system of particles moving on a one-dimensional lattice. Particles tend to separate from each other, and evolution ceases when at least one empty site is found between any two…
... but no other surprises in the zero range world. We check all nearest neighbour 1-dimensional asymmetric zero range processes for random walking product shock measures as demonstrated already for a few cases in the literature. We find…
We consider an extension of the zero-range process to the case where the hop rate depends on the state of both departure and arrival sites. We recover the misanthrope and the target process as special cases for which the probability of the…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
Single-file transport, where particles diffuse in narrow channels while not overtaking each other, is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous…
We establish an invariance principle for a one-dimensional random walk in a dynamical random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite…
We consider the symmetric simple exclusion system on $\mathbb{Z}^d$, $d \ge 2$, starting from a class of ``step'' initial conditions in which particles are constrained within a half-space. One may count the number $N_t$ of particles that…
We consider the large deviations of the hydrodynamic rescaling of the zero-range process on $\mathbb{Z}^d$ in any dimension $d\ge 1$. Under mild and canonical hypotheses on the local jump rate, we obtain matching upper and lower bounds,…
We study the asymmetric zero-range process (ZRP) with L sites and open boundaries, conditioned to carry an atypical current. Using a generalized Doob h-transform we compute explicitly the transition rates of an effective process for which…
We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…
The recently introduced correspondence between one-dimensional two-species driven models and the Zero-Range Process is extended to study the case where the densities of the two species need not be equal. The correspondence is formulated…
We study a zero-range process where the jump rates do not only depend on the local particle configuration, but also on the size of the system. Rigorous results on the equivalence of ensembles are presented, characterizing the occurrence of…
We introduce a simple zero-range process with constant rates and one fast rate for a particular occupation number, which diverges with the system size. Surprisingly, this minor modification induces a condensation transition in the…
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…
We present a one-dimensional nonlocal hopping model with exclusion on a ring. The model is related to the Raise and Peel growth model. A nonnegative parameter $u$ controls the ratio of the local backwards and nonlocal forwards hopping…
This paper analyses the impact of collisions in a system of $N$ identical hard-core particles driven according to a velocity jump process. The physical space is essentially a channel in $\mathbb{R}$ with a probability of occupants being…
We study the adsorption and desorption kinetics of interacting particles moving on a one-dimensional lattice. Confinement is introduced by limiting the number of particles on a lattice site. Adsorption and desorption are found to proceed at…