Related papers: SLE_k growth processes and conformal field theorie…
We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents…
This paper reviews selected aspects of the growth of cosmological structure, covering the following general areas: (1) expected characteristics of linear density perturbations according to various candidate theories for the origin of…
Many real phenomena may be modelled as locally finite unions of $d$-dimensional time dependent random closed sets in $\mathbb{R}^d$, described by birth-and-growth stochastic processes, so that their mean volume and surface densities, as…
Random processes with stationary increments and intrinsic random processes are two concepts commonly used to deal with non-stationary random processes. They are broader classes than stationary random processes and conceptually closely…
Starting from certain causality conditions and a discrete form of general covariance, we derive a very general family of classically stochastic, sequential growth dynamics for causal sets. The resulting theories provide a relatively…
In this chapter 2 of the e-book "Self-Organized Criticality Systems" we summarize the classical cellular automaton models, which consist of a statistical aspect that is universal to all SOC systems, and a physical aspect that depends on the…
We develop statistical mechanics for stochastic growth processes as applied to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and…
Through appropriate projections of an exact renormalization group equation, we study fixed points, critical exponents and nontrivial renormalization group flows in scalar field theories in $2<d<4$. The standard upper critical dimensions…
The mean growth rate of the state vector is evaluated for a generalized linear stochastic second-order system with a symmetric matrix. Diagonal entries of the matrix are assumed to be independent and exponentially distributed with different…
The paper is concerned with stochastic approximation procedures having three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We…
We consider a stochastic model, describing the growth of two competing infections on $\mathbb{R}^d$. The growth takes place by way of spherical outbursts in the infected region, an outburst in the type 1 (2) infected region causing all…
We study the flocking model introduced by Vicsek in the "coarsening" regime. At standard self-propulsion speeds, we find two distinct growth laws for the coupled density and velocity fields. The characteristic length scale of the density…
The purpose of the present work is twofold. First, we develop the theory of general self-similar growth-fragmentation processes by focusing on martingales which appear naturally in this setting and by recasting classical results for…
Up to now the raise and peel model was the single known example of a one-dimensional stochastic process where one can observe conformal invariance. The model has one-parameter. Depending on its value one has a gapped phase, a critical point…
The influence of a random environment on the dynamics of a fluctuating rough surface is investigated using a field theoretic renormalization group. The environment motion is modelled by the stochastic Navier--Stokes equation, which includes…
We analyze the bootstrap percolation process on the stochastic block model (SBM), a natural extension of the Erd\"{o}s--R\'{e}nyi random graph that allows representing the "community structure" observed in many real systems. In the SBM,…
Spontaneous stratification of granular mixtures has been reported by Makse et al. [Nature 386, 379 (1997)] when a mixture of grains differing in size and shape is poured in a quasi-two-dimensional heap. We study this phenomenon using two…
A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions…
The phenomenon of stochastic growth of a surface on a two-dimensional substrate occurs in Nature in a variety of circumstances and its statistical characterization requires the study of higher order cumulants. Here, we consider the…
Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion…