Related papers: Existence of the zero range process and a depositi…

We study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The main properties of such branching…

In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…

Consider the mutually catalytic branching process with finite branching rate $\gamma$. We show that as $\gamma\to\infty$, this process converges in finite-dimensional distributions (in time) to a certain discontinuous process. We give…

A subshift with linear block complexity has at most countably many ergodic measures, and we continue of the study of the relation between such complexity and the invariant measures. By constructing minimal subshifts whose block complexity…

A one dimensional exclusion process is introduced where particles hop to a neighbouring vacant site with a rate that depends on the size of the block they belong to. This model is equivalent to a zero range process (ZRP) and shares the same…

We consider the evolution by crystalline curvature of a planar set in a stratified medium, modeled by a periodic forcing term. We characterize the limit evolution law as the period of the oscillations tends to zero. Even if the model is…

Let $r: S\times S\to \bb R_+$ be the jump rates of an irreducible random walk on a finite set $S$, reversible with respect to some probability measure $m$. For $\alpha >1$, let $g: \bb N\to \bb R_+$ be given by $g(0)=0$, $g(1)=1$, $g(k) =…

Here we prove that for dilatation structures linearity (see arXiv:0705.1440v1) is equivalent to a statement about the inverse semigroup generated by the family of dilatations of the space. The result is new for Carnot groups and the proof…

We prove the uniform in space and time convergence of the scaled heights of large classes of deterministic growth models that are monotone and equivariant under translations by constants. The limits are characterized as the unique…

Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility…

We consider generic finite range percolation models on $\mathbb{Z}^d$ under a high temperature assumption (exponential decay of connection probabilities and exponential ratio weak mixing). We prove that the rate of decay of point-to-point…

For the one dimensional infinite group relaxation, we construct a sequence of extreme valid functions that are piecewise linear and such that for every natural number $k\geq 2$, there is a function in the sequence with $k$ slopes. This…

During the last decade, self-affine geometrical properties of many growing aggregates, originated in a wide variety of processes, have been well characterized. However, little progress has been achieved in the search of a unified…

We obtain new bounds for the optimal matching cost for empirical measures with unbounded support. For a large class of radially symmetric and rapidly decaying probability laws, we prove for the first time the asymptotic rate of convergence…

It is shown that an alternative approach for the characterization of growing branched patterns consists of the statistical analysis of frozen structures, which cannot be modified by further growth, that arise due to competitive processes…

Singularities appear in numerous important mathematical models used in Physics. And in most of such cases singularities are involved in essentially nonlinear contexts. For more than four decades, general enough nonlinear theories of…

Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. This representation is based upon a triangular matrix of transition rates. We expand the state vector of mass multiplicities, which…

We study the zero-range process on the complete graph. It is a Markov chain model for a microcanonical ensemble. We prove that the process converges to a fluid limit. The fluid limit rapidly relaxes to the appropriate Gibbs distribution.

We consider a branching-selection particle system on the real line. In this model the total size of the population at time $n$ is limited by $\exp\left(a n^{1/3}\right)$. At each step $n$, every individual dies while reproducing…

In order to model random density-dependence in population dynamics, we construct the random analogue of the well-known logistic process in the branching process' framework. This density-dependence corresponds to intraspecific competition…