Related papers: A growth model in multiple dimensions and the heig…
We prove a hydrodynamic limit for ballistic deposition on a multidimensional lattice. In this growth model particles rain down at random and stick to the growing cluster at the first point of contact. The theorem is that if the initial…
We study here a standard next-nearest-neighbor (NNN) model of ballistic growth on one- and two-dimensional substrates focusing our analysis on the probability distribution function $P(M,L)$ of the number $M$ of maximal points (i.e., local…
Finding the most powerful node in a dynamic random network, the largest set in a partition-valued stochastic process, or the largest family in an evolving population at a given time, can be a very difficult problem. This is particularly the…
We present an explicit construction of a Markovian random growth process on integer partitions such that given it visits some level $n$, it passes through any partition $\lambda$ of $n$ with equal probabilities. The construction has…
We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its…
We consider Robinson-Schensted-Knuth algorithm applied to a random input and study the growth of the bottom rows of the corresponding Young diagrams. We prove multidimensional Poisson limit theorem for the resulting Plancherel growth…
The Gompertz model describes the growth in time of the size of significant quantities associated to a large number of systems, taking into account nonlinearity features by a linear equation satisfied by a nonlinear function of the size.…
A construction as a growth process for sampling of the uniform infinite planar triangulation (UIPT), defined in a previous paper, is given. The construction is algorithmic in nature, and is an efficient method of sampling a portion of the…
We introduce a second-order stochastic model to explore the variability in growth of biological shapes with applications to medical imaging. Our model is a perturbation with a random force of the Hamiltonian formulation of the geodesics.…
Let $\mathcal{P}_{\lambda}:=\mathcal{P}_{\lambda\kappa}$ denote a Poisson point process of intensity $\lambda\kappa$ on $[0,1]^d,d\geq2$, with $\kappa$ a bounded density on $[0,1]^d$ and $\lambda\in(0,\infty)$. Given a closed subset…
From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Is every point contained in balloons infinitely often or not? We answer this for the Euclidean space, the…
In this review paper we consider the polynuclear growth (PNG) model in one spatial dimension and its relation to random matrix ensembles. For curved and flat growth the scaling functions of the surface fluctuations coincide with limit…
We study the porous medium equation (PME) in one space dimension in presence of additive non-conservative white noise, and interpreted as a stochastic growth equation for the height field of an interface. We predict the values of the two…
We investigate the limiting behaviour of the path of random bridges treated as random sets in $\mathbb{R}^{d}$ with the Euclidean metric and the dimension $d$ increasing to infinity. The main result states that, in the square integrable…
Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…
In many growth processes particles are highly mobile in an active layer at the surface, but are relatively immobile once incorporated in the bulk. We study models in which atoms are allowed to interact, equilibrate, and order on the…
We study the joint probability distribution function (pdf) of the maximum M of the height and its position X_M of a curved growing interface belonging to the universality class described by the Kardar-Parisi-Zhang equation in 1+1…
We study the asymptotic scaling properties of a massively parallel algorithm for discrete-event simulations where the discrete events are Poisson arrivals. The evolution of the simulated time horizon is analogous to a non-equilibrium…
We study a generalization of the Wolf-Villain (WV) interface growth model based on a probabilistic growth rule. In the WV model, particles are randomly deposited onto a substrate and subsequently move to a position nearby where the binding…
We present two constructions, both inspired by ideas from graph theory, of sequences random surfaces of growing area, whose systoles grow logarithmically as a function of their area. This also allows us to prove a new lower bound on the…