What is the scaling limit of diffusion-limited aggregation (DLA) in the plane? This is an old
and famously difficult question. One can generalize the question in two ways: first, one may …

Let each of $ n $ particles starting at the origin in $\mathbb Z^ 2$ perform simple random
walk until reaching a site with no other particles. Lawler, Bramson, and Griffeath proved that …

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 …

Abstract Activated Random Walk (ARW) is an interacting particle system on the d-
dimensional lattice Z d. On a finite subset V⊂ Z d it defines a Markov chain on {0, 1} V. We …

In previous works, we showed that the internal diffusion-limited aggregation (DLA) cluster on
Z d with t particles is almost surely spherical up to a maximal error of O (log t) if d= 2 and O …

Laplacian growth is the study of interfaces that move in proportion to harmonic measure.
Physically, it arises in fluid flow and electrical problems involving a moving boundary. We …

The term free boundary problem (FBP) refers, in the modern applied mathematical literature,
to a problem in which one or several variables must be determined in different domains of …

The divisible sandpile starts with iid random variables (“masses”) at the vertices of an
infinite, vertex-transitive graph, and redistributes mass by a local toppling rule in an attempt …

Harmonic balls are domains that satisfy the mean‐value property for harmonic functions. We
establish the existence and uniqueness of harmonic balls on Liouville quantum gravity …

Internal diffusion-limited aggregation with uniform starting points Page 1 www.imstat.org/aihp
Annales de l’Institut Henri Poincaré - Probabilités et Statistiques 2020, Vol. 56, No. 1, 391–404 …