Related papers: On Diffusion Limited Deposition
We identify sources of systematic error in traditional simulations of the Witten-Sander model of diffusion-limited aggregation (DLA) on a square lattice. We present an algorithm that reduces these biases to below $10^{-12}$. We grow…
When sand flows out of a funnel onto a surface, a three dimensional pile that is stabilized by friction grows taller as it spreads. Here we investigate an idealized two dimensional analogue: spreading of a pile of monodisperse oil droplets…
Random walkers absorbing on a boundary sample the Harmonic Measure linearly and independently: we discuss how the recurrence times between impacts enable non-linear moments of the measure to be estimated. From this we derive a new technique…
The results of the computer simulation of the aggregates growth of the similarly charged particles in the framework of deterministic Laplacian growth model on a square lattice are presented. Cluster growth is controlled by three parameters…
The growth exponent $\alpha$ for loop-erased or Laplacian random walk on the integer lattice is defined by saying that the expected time to reach the sphere of radius $n$ is of order $n^\alpha$. We prove that in two dimensions, the growth…
We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding…
Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence that can have long-range dependence. In this paper, we find the scaling limit of a random walk that follows GBP. The result is a new class of…
We study a stochastic Laplacian growth model, where a set $\mathbf{U}\subseteq\mathbb{R}^{\mathrm{d}}$ grows according to a reflecting Brownian motion in $\mathbf{U}$ stopped at level sets of its boundary local time. We derive a scaling…
Through the analysis of unbiased random walks on fractal trees and continuous time random walks, we show that even if a process is characterized by a mean square displacement (MSD) growing linearly with time (standard behaviour) its…
The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…
We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…
The percolation behaviour during the deposit formation, when the spanning cluster was formed in the substrate plane, was studied. Two competitive or mixed models of surface layer formation were considered in (1+1)-dimensional geometry.…
The Metropolis-adjusted Langevin (MALA) algorithm is a sampling algorithm which makes local moves by incorporating information about the gradient of the logarithm of the target density. In this paper we study the efficiency of MALA on a…
Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived…
It had been conjectured that Diffusion Limited Aggregates and Laplacian Growth patterns (with small surface tension) are in the same universality class. Using iterated conformal maps we construct a 1-parameter family of fractal growth…
We consider the penetration length $l$ of random walkers diffusing in a medium of perfect or imperfect absorbers of number density $\rho$. We solve this problem on a lattice and in the continuum in all dimensions $D$, by means of a…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
An extended polymer collapses to form a globule when subjected to a quench below the collapse transition temperature. The process begins with the formation of clusters of monomers or ``pearls''. The nascent clusters merge, resulting in…
We consider discrete-time branching random walks with a radially symmetric distribution. Independently of each other individuals generate offspring whose relative locations are given by a copy of a radially symmetric point process…
We use cosmological hydrodynamical simulations including star formation and metal enrichment to study the evolution of the chemical properties of galaxy-like objects at high redshift in the range $0.25<z< 2.35$ in a hierarchical clustering…