Related papers: Zero-range processes with rapidly growing rates
We consider birth-and-death processes of objects (animals) defined in ${\bf Z}^d$ having unit death rates and random birth rates. For animals with uniformly bounded diameter we establish conditions on the rate distribution under which the…
O(N)-symmetric lattice scalar fields are considered, coupled to a chemical potential and source terms. At the example of N=2, it is shown that such systems can even in (0+1) dimensions produce infinite-range correlations and a non-zero…
We introduce and solve exactly a class of interacting particle systems in one dimension where particles hop asymmetrically. In its simplest form, namely asymmetric zero range process (AZRP), particles hop on a one dimensional periodic…
The paper discusses two models for non-overlapping finite line-segments constructed via the lilypond protocol, operating here on a given array of points in the plane with which are associated directions. At time 0, each line-segment starts…
A method of constructing an entire function with given zeros and estimates of growth is suggested. It gives a possibility to describe zero sets of certain classes of entire functions of one and several variables in terms of growth of volume…
A free zero-range process (FRZP) is a simple stochastic process describing the dynamics of a gas of particles hopping between neighboring nodes of a network. We discuss three different cases of increasing complexity: (a) FZRP on a rigid…
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…
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 a driven zero range process which models a closed system of attractive particles that hop with site-dependent rates and whose steady state shows a condensation transition with increasing density. We characterise the dynamical…
We introduce a stochastic model of growing networks where both, the number of new nodes which joins the network and the number of connections, vary stochastically. We provide an exact mapping between this model and zero range process, and…
We consider a class of stochastic growth models on the integer lattice which includes various interesting examples such as the number of open paths in oriented percolation and the binary contact path process. Under some mild assumptions, we…
Zero-range processes with decreasing jump rates are well known to exhibit a condensation transition under certain conditions on the jump rates, and the dynamics of this transition continues to be a subject of current research interest.…
We consider a non-conserving zero-range process with hopping rate proportional to the number of particles at each site. Particles are added to the system with a site-dependent creation rate, and removed from the system with a uniform…
The aim of these lecture notes is a description of the statics and dynamics of zero-range processes and related models. After revisiting some conceptual aspects of the subject, emphasis is then put on the study of the class of zero-range…
Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two-dimensions. We find that the synchronization landscape (corresponding to the…
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…
Real-world growth processes and scalings have been broadly categorized into three growth regimes with distinctly different properties and driving forces. The first two are characterized by a positive and constant feedback between growth and…
Optimal growth of structures governed by spatially stochastic dynamics arises in many scientific settings, for example in processes such as solution-based crystallization and the formation of microbial biofilms on patterned substrates or…
For a class of one-dimensional mass transport models we present a simple and direct test on the chipping functions, which define the probabilities for mass to be transferred to neighbouring sites, to determine whether the stationary…
We consider the mean-field Zero-Range process in the regime where the potential function $r$ is increasing to infinity at sublinear speed, and the density of particles is bounded. We determine the mixing time of the system, and establish…