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Related papers: Internal Aggregation Models on Comb Lattices

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We study internal diffusion limited aggregation (DLA) on the two dimensional comb lattice. The comb lattice is a spanning tree of the euclidean lattice, and internal DLA is a random growth model, where simple random walks, starting one at a…

Probability · Mathematics 2014-01-28 Amine Asselah , Houda Rahmani

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 consider a cluster growth model on the d-dimensional lattice, called internal diffusion limited aggregation (internal DLA). In this model, random walks start at the origin, one at a time, and stop moving when reaching a site not occupied…

Probability · Mathematics 2013-06-03 Amine Asselah , Alexandre Gaudilliere

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 investigate three types of Internal Diffusion Limited Aggregation (IDLA) models. These models are based on simple random walks on $\mathbf{Z}^2$ with infinitely many sources that are the points of the vertical axis…

Probability · Mathematics 2025-10-17 Nicolas Chenavier , David Coupier , Arnaud Rousselle

We consider a cluster growth model on Z^d, called internal diffusion limited aggregation (internal DLA). In this model, random walks start at the origin, one at a time, and stop moving when reaching a site not occupied by previous walks. It…

Probability · Mathematics 2010-05-31 Amine Asselah , Alexandre Gaudilliere

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 consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when…

Probability · Mathematics 2013-05-27 Amine Asselah , Alexandre Gaudillière

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

Internal diffusion-limited aggregation (IDLA) is a stochastic growth model on a graph $G$ which describes the formation of a random set of vertices growing from the origin (some fixed vertex) of $G$. Particles start at the origin and…

Probability · Mathematics 2020-08-26 Joe P. Chen , Wilfried Huss , Ecaterina Sava-Huss , Alexander Teplyaev

Internal diffusion-limited aggregation is a growth model based on random walk in Z^d. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family of walks in Z^2 for which the limiting shape is a…

Probability · Mathematics 2010-08-17 Wouter Kager , Lionel Levine

We consider the internal diffusion limited aggregation (IDLA) process on the infinite cluster in supercritical Bernoulli bond percolation on Euclidean lattices. It is shown that the process on the cluster behaves like it does on the…

Probability · Mathematics 2010-05-25 Eric Shellef

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

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

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

Internal DLA (IDLA) is an internal aggregation model in which particles perform random walks from the origin, in turn, and stop upon reaching an unoccupied site. Levine and Peres showed that, when particles start instead from fixed…

Probability · Mathematics 2022-01-24 David Darrow

Internal diffusion limited aggregation (IDLA) is a random aggregation model on a graph $G$, whose clusters are formed by random walks started in the origin (some fixed vertex) and stopped upon visiting a previously unvisited site. On the…

Probability · Mathematics 2022-02-04 Nico Heizmann

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 rotor-router aggregation on the square lattice Z^2, particles starting at the origin perform deterministic analogues of random walks until reaching an unoccupied site. The limiting shape of the cluster of occupied sites is a disk. We…

Combinatorics · Mathematics 2011-09-28 Wouter Kager , Lionel Levine

In a recent paper (Bogoyavlenskiy V A 2002 \JPA \textbf{35} 2533), an algorithm aiming to generate isotropic clusters of the on-lattice diffusion-limited aggregation (DLA) model was proposed. The procedure consists of aggregation…

Statistical Mechanics · Physics 2007-05-23 S. G. Alves , S. C. Ferreira
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