Related papers: Random growth models: shape and convergence rate
This is a brief survey of laws of large numbers, fluctuation results and large deviation principles for asymmetric interacting particle systems that represent moving interfaces on the plane. We discuss the exclusion process, the Hammersley…
We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in…
We study in this paper, the first passage percolation on a random graph model, the configuration model. We first introduce, the notions of weighted diameter, which is the maximum of the weighted lengths of all optimal paths between any two…
We consider a last passage percolation model in dimension $1+1$ with potential given by the product of a spatial i.i.d. potential with symmetric bounded distribution and an independent i.i.d. in time sequence of signs. We assume that the…
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…
Critical, or scale independent, systems are so ubiquitous, that gaining theoretical insights on their nature and properties has many direct repercussions in social and natural sciences. In this report, we start from the simplest possible…
A growing random graph is constructed by successively sampling without replacement an element from the pool of virtual vertices and edges. At start of the process the pool contains $N$ virtual vertices and no edges. Each time a vertex is…
Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a…
The Newman-Watts model is given by taking a cycle graph of n vertices and then adding each possible edge $(i,j), |i-j|\neq 1 \mod n$ with probability $\rho/n$ for some $\rho>0$ constant. In this paper we add i.i.d. exponential edge weights…
We consider connectivity properties of certain i.i.d. random environments on $\Z^d$, where at each location some steps may not be available. Site percolation and oriented percolation can be viewed as special cases of the models we consider.…
We provide a general framework to study stochastic sequences related to individual learning in economics, learning automata in computer sciences, social learning in marketing, and other applications. More precisely, we study the asymptotic…
We construct a family of stochastic growth models in 2+1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1+1 dimensional growth models in the KPZ class and random tiling models. We show…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
In this work we study a tissue growth model with applications to tumour growth. The model is based on that of Perthame, Quir\'os, and V\'azquez proposed in 2014 but incorporates the advective effects caused, for instance, by the presence of…
A random graph evolution based on the interactions of N vertices is studied. During the evolution both the preferential attachment method and the uniform choice of vertices are allowed. The weight of a vertex means the number of its…
I consider how cell shape and environmental geometry affect the rate of nutrient capture and the consequent maximum growth rate of a cell, focusing on rod-like species like \textit{E.\ coli}. Simple modeling immediately implies that it is…
We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…
An important question in biology is how the relative size of different organs is kept nearly constant during growth of an animal. This property, called proportionate growth, has received increased attention in recent years. We discuss our…
An Euclidean first-passage percolation (FPP) model describing the competing growth between $k$ different types of infection is considered. We focus on the long time behavior of this multi-type growth process and we derive multi-type shape…
We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually…