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Let each of n particles starting at the origin in Z2 perform simple random walk until reaching a site with no other particles. Lawler, Bramson, and Griffeath proved that the resulting random set A(n) ...
Let A(t) denote the cluster produced by internal diffusion limited aggregation (internal DLA) with t particles in dimension d ≥ 3. We show that A(t) is approximately spherical, up to an O(√log t) erro...
In previous works, we showed that the internal DLA cluster on Zd with t particles is almost surely spherical up to a maximal error of O(log t) if d = 2 and O(√log t) if d ≥ 3. This paper addresses “av...
Let A(t) denote the cluster produced by internal di usion limited aggregation (internal DLA) with t particles in dimension d 3. We show that A(t) is approximately spherical, up to an O(
p log t) er...
We consider internal diffusion limited aggregation in dimension larger or equal to two. This is a random cluster growth model, where random walks start at the origin of the $d$-dimensional lattice, o...
From logarithmic to subdiffusive polynomial fluctuations for internal DLA and related growth models
internal diffusion limited aggregation cluster growth
2010/12/6
We consider a family of cluster growth models on Zd, which generalize internal diffusion limited aggregation (internal DLA). The latter model is simplest to describe:random walks start at the origin, ...