منابع مشابه
Rotor-Router Aggregation on the Comb
We prove a shape theorem for rotor-router aggregation on the comb, for a specific initial rotor configuration and clockwise rotor sequence for all vertices. Furthermore, as an application of rotor-router walks, we describe the harmonic measure of the rotor-router aggregate and related shapes, which is useful in the study of other growth models on the comb. We also identify the shape for which t...
متن کاملRotor-Router Aggregation on the Layered Square Lattice
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 cluster of occupied sites is a disk. We consider a small change to the routing mechanism for sites on the xand y-axes, resulting in a limiting shape which is a diamond instead of a disk. We show that f...
متن کاملThe Rotor-Router Model
Building on earlier work of Diaconis and Fulton (1991) and Lawler, Bramson, and Griffeath (1992), Propp in 2001 defined a deterministic analogue of internal diffusion-limited aggregation. This growth model is a ”convergent game” of the sort studied by Eriksson (1996). In one dimension, we show that the model is equivalent to a simple dynamical system with three integer-valued parameters; an inv...
متن کاملThe rotor-router model on regular trees
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 show that the set of occupied sites for this model on an infinite regular tree is a perfect ball whenever it can be, provided the initial rotor configuration is acyclic (that is, no two neighboring vertices have rotors pointing to one another). T...
متن کاملRecurrent Rotor-Router Configurations
We prove the existence of recurrent initial configurations for the rotor walk on many graphs, including Zd, and planar graphs with locally finite embeddings. We also prove that recurrence and transience of rotor walks are invariant under changes in the starting vertex and finite changes in the initial configuration.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2011
ISSN: 1077-8926
DOI: 10.37236/711