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We investigate diffusion-limited aggregation (DLA) in a wedge geometry. Arneodo and collaborators have suggested that the ensemble average of DLA cluster density should be close to the noise-free selected Saffman-Taylor finger. We show that…

Statistical Mechanics · Physics 2009-11-11 Leonard M. Sander , Ellak Somfai

In the classical model of Diffusion Limited Aggregation (DLA), introduced by Witten and Sander, the process begins with a single particle cluster placed at the origin of a space, and then, one at a time, particles make a random walk from…

Probability · Mathematics 2026-04-29 Colin Cooper , Alan Frieze

Models of fractal growth commonly consider particles diffusing in a medium and that stick irreversibly to the forming aggregate when making contact for the first time. As shown by the well-known diffusion limited aggregation (DLA) model and…

Statistical Mechanics · Physics 2023-10-19 Uriel Villanueva-Alcalá , José R. Nicolás-Carlock , Denis Boyer

We study the scaling limits of three different aggregation models on Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform deterministic analogues of…

Probability · Mathematics 2010-12-24 Lionel Levine , Yuval Peres

We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps. We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this…

Probability · Mathematics 2013-06-20 Gideon Amir , Omer Angel , Gady Kozma

Diffusion Limited Aggregation (DLA) is a model of fractal growth that was introduced in 1981 and had since attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. Despite…

Statistical Mechanics · Physics 2007-05-23 Benny Davidovich , Itamar Procaccia

We show that Internal Diffusion Limited Aggregation (IDLA) on $\mathbb{Z}^d$ has near optimal Cheeger constant when the growing cluster is large enough. This implies, through a heat kernel lower bound derived previously in [H], that simple…

Probability · Mathematics 2019-04-18 Ruojun Huang

We study the scaling limits of three different aggregation models on the integer lattice Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform…

Probability · Mathematics 2007-12-31 Lionel Levine

We study the following growth model on a regular d-ary tree. Points at distance n adjacent to the existing subtree are added with probabilities proportional to alpha^{-n}, where alpha<1 is a positive real parameter. The heights of these…

Probability · Mathematics 2007-05-23 MArtin T. Barlow , Robin Pemantle , Edwin A. Perkins

The Internal Diffusion Limited Aggregation has been introduced by Diaconis and Fulton in 1991. It is a growth model defined on an infinite set and associated to a Markov chain on this set. We focus here on sets which are finitely generated…

Probability · Mathematics 2007-05-23 Sebastien Blachere , Sara Brofferio

For a class of aggregation models on the integer lattice $\mathbb{Z}^d$, $d\geq 2$, in which clusters are formed by particles arriving one after the other and sticking irreversibly where they first hit the cluster, including the classical…

Probability · Mathematics 2023-08-28 Tillmann Bosch , Steffen Winter

Internal Diffusion Limited Aggregation (IDLA) is a model that describes the growth of a random aggregate of particles from the inside out. Shellef proved that IDLA processes on supercritical percolation clusters of integer-lattices fill…

Probability · Mathematics 2011-11-03 Hugo Duminil-Copin , Cyrille Lucas , Ariel Yadin , Amir Yehudayoff

We propose a simple model of columnar growth through {\it diffusion limited aggregation} (DLA). Consider a graph $G_N\times\N$, where the basis has $N$ vertices $G_N:=\{1,\dots,N\}$, and two vertices $(x,h)$ and $(x',h')$ are adjacent if…

Probability · Mathematics 2015-11-24 A. Asselah , E. Cirillo , E. Scoppola , B. Scoppola

We study two random processes on an $n$-vertex graph inspired by the internal diffusion limited aggregation (IDLA) model. In both processes $n$ particles start from an arbitrary but fixed origin. Each particle performs a simple random walk…

Discrete Mathematics · Computer Science 2019-11-27 Nicolas Rivera , Alexandre Stauffer , Thomas Sauerwald , John Sylvester

Diffusion-limited aggregation has a natural generalization to the "$\eta$-models", in which $\eta$ random walkers must arrive at a point on the cluster surface in order for growth to occur. It has recently been proposed that in spatial…

Statistical Mechanics · Physics 2009-11-07 Thomas C. Halsey

In this paper, we analyze the scaling properties of a model that has as limiting cases the diffusion-limited aggregation (DLA) and the ballistic aggregation (BA) models. This model allows us to control the radial and angular scaling of the…

Statistical Mechanics · Physics 2010-09-09 S. G. Alves , S. C. Ferreira

Predicting urban growth is important for practical reasons, and also for the challenge it presents to theoretical frameworks for cluster dynamics. Recently, the model of diffusion limited aggregation (DLA) has been applied to describe urban…

Condensed Matter · Physics 2007-05-23 Hernan A. Makse , Shlomo Havlin , H. Eugene Stanley

Irreversible diffusion limited cluster aggregation (DLCA) of hard spheres was simulated using Brownian cluster dynamics. Bound spheres were allowed to move freely within a specified range, but no bond breaking was allowed. The structure and…

Soft Condensed Matter · Physics 2009-03-25 Sujin Babu , Jean-Christophe Gimel , Taco Nicolai

A theoretical model for fractal growth of DLA-clusters in two- and three-dimensional Euclidean space is proposed. This model allows to study some statistical properties of growing clusters in two different situations: in the static case…

Chaotic Dynamics · Physics 2007-05-23 A. Loskutov , D. Andrievsky , V. Ivanov , K. Vasiliev , A. Ryabov

We investigate the diffusion limited aggregation of particles executing persistent random walks. The scaling properties of both random walks and large aggregates are presented. The aggregates exhibit a crossover between ballistic and…

Statistical Mechanics · Physics 2011-07-28 Isadora R. Nogueira , Sidiney G. Alves , Silvio C. Ferreira