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Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile
Strong Spherical Asymptotics Rotor-Router Aggregation Divisible Sandpile
2015/8/14
The rotor-router model is a deterministic analogue of random walk.It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a...
Scaling Limits for Internal Aggregation Models with Multiple Sources
Scaling Limits Internal Aggregation Models Multiple Sources
2015/8/14
We study the scaling limits of three different aggregation models on Zd: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which parti...
DIAMOND AGGREGATION
DIAMOND AGGREGATION
2015/8/14
Internal diffusion-limited aggregation is a growth model based on random walk in Zd. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family of walks in...
ROTOR-ROUTER AGGREGATION ON THE LAYERED SQUARE LATTICE
ROTOR-ROUTER AGGREGATION LAYERED SQUARE LATTICE
2015/8/14
In rotor-router aggregation on the square lattice Z2, particles starting at the origin perform deterministic analogues of random walks until reaching an unoccupied site. The limiting shape of the clus...
Oil and water:a two-type internal aggregation model
Oil and water internal aggregation model
2015/8/14
We introduce a two-type internal DLA model which is an example of a non-unary abelian network. Starting with n “oil” and n “water” particles at the origin, the particles diffuse in Z according to the ...
We study the scaling limits of three different aggregation models on Zd: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which parti...