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Let A(t) denote the cluster produced by internal diffusion limited aggregation (internal DLA) with t particles in dimension d > 2. We show that A(t) is approximately spherical, up to an O(\sqrt{\log t}) error.

Probability · Mathematics 2011-02-01 David Jerison , Lionel Levine , Scott Sheffield

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

A diffusion-limited aggregation process, in which clusters coalesce by means of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a heuristic argument that predicts logarithmic corrections to the mean-field asymptotic…

Condensed Matter · Physics 2009-10-22 P. L. Krapivsky

We study internal diffusion limited aggregation on $\mathbb{Z}$, where a cluster is grown incrementally by adding, for each random walk dispatched from the origin, the first site it reaches outside the cluster. We assume that the increment…

Probability · Mathematics 2026-03-11 Conrado da Costa , Debleena Thacker , Andrew Wade

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

We prove that the one dimensional Multi-Particle Diffusion Limited Aggregation model has linear growth whenever the particle density exceeds 1 answering a question of Kesten and Sidoravicius. As a corollary we prove linear growth in all…

Probability · Mathematics 2016-09-27 Allan Sly

Several models based on the diffusion-limited aggregation (DLA) model were proposed and their scaling properties explored by computational and theoretical approaches. In this paper, we consider a new extension of the on-lattice DLA model in…

Statistical Mechanics · Physics 2009-11-10 S. C. Ferreira

Diffusion limited aggregation (DLA) is a well studied phenomenon in which diffusing particles cumulatively aggregate on a starting fixed seed point, forming a pattern which is fractal in structure. Here we report an interesting DLA process…

Pattern Formation and Solitons · Physics 2025-04-21 Suvrajyoti Chatterjee , Saba Firoze , Tabish Qureshi

Diffusion-Limited Aggregation (DLA), the canonical model for non-equilibrium fractal growth, emerges from the simple rule of irreversible attachment by random walkers. Despite four decades of study, a unified computational framework…

Statistical Mechanics · Physics 2026-01-07 Satish Prajapati

Cylindrical lattice diffusion limited aggregation (DLA), with a narrow width N, is solved for site-sticking conditions using a Markovian matrix method (which was previously developed for the bond-sticking case). This matrix contains the…

Statistical Mechanics · Physics 2009-10-31 Boaz Kol , Amnon Aharony

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

A parallel algorithm for ``diffusion-limited aggregation'' (DLA) is described and analyzed from the perspective of computational complexity. The dynamic exponent z of the algorithm is defined with respect to the probabilistic parallel…

comp-gas · Physics 2016-08-31 K. Moriarty , J. Machta , R. Greenlaw

We study the diffusion of a particle with a time-dependent diffusion constant $D(t)$ that switches between random values drawn from a distribution $W(D)$ at a fixed rate $r$. Using a renewal approach, we compute exactly the moments of the…

Statistical Mechanics · Physics 2025-08-06 Mathis Guéneau , Satya N. Majumdar , Gregory Schehr

We consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than $\pi/4$, there is some $a>2$ such that almost surely, for all $R$ large enough, after time $R^a$ all new…

Probability · Mathematics 2018-04-13 Eviatar B. Procaccia , Ron Rosenthal , Yuan Zhang

We introduce a lattice gas model of cluster growth via the diffusive aggregation of particles in a closed system obeying a local, deterministic, microscopically reversible dynamics. This model roughly corresponds to placing the irreversible…

Statistical Mechanics · Physics 2009-10-31 Raissa M. D'Souza , Norman H. Margolus

We develop the skeleton algorithm to define the number of main branches $N_b$ of diffusion-limited aggregation (DLA) clusters. The skeleton algorithm provides a systematic way to remove dangling side branches of the DLA cluster and has…

Condensed Matter · Physics 2009-10-28 Stefan Schwarzer , Shlomo Havlin , Peter Ossadnik , H. Eugene Stanley

We discuss the scaling of characteristic lengths in diffusion limited aggregation (DLA) clusters in light of recent developments using conformal maps. We are led to the conjecture that the apparently anomalous scaling of lengths is due to…

Statistical Mechanics · Physics 2009-10-31 E. Somfai , L. M. Sander , R. C. Ball

Internal Diffusion Limited Aggregation is an interacting particle system that describes the growth of a random cluster governed by the boundary harmonic measure seen from an internal point. Our paper studies IDLA in $\mathbb{Z}^d$ driven by…

Probability · Mathematics 2025-10-16 Amine Asselah , Vittoria Silvestri , Lorenzo Taggi

We present and study the Pool model in $\mathbb{R}^2$, a rotationally symmetric analogue of Multi-Particle Diffusion-Limited Aggregation (MDLA), in which particles ("droplets") perform continuous-time random walks and are absorbed upon…

Probability · Mathematics 2026-04-17 Zhenhao Cai , Eviatar B. Procaccia , Yuan Zhang

In this work, the transition between diffusion-limited and ballistic aggregation models was revisited using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter $\lambda$, which…

Statistical Mechanics · Physics 2009-11-11 S. C. Ferreira , S. G. Alves , A. Faissal Brito , J. G. Moreira