منابع مشابه
Recurrent 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.
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...
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Programmable networks offer the ability to customize router behaviour at run time, thus increasing flexibility of network administration. Programmable network routers are configured using domain-specific languages. The ability to evolve router programs dynamically creates potential for misconfigurations. By exploiting domain-specific abstractions, we are able to translate router configurations ...
متن کاملRotor-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 کاملThe Rotor-Router Shape is Spherical
In the two-dimensional rotor-router walk (defined by Jim Propp and presented beautifully in [4]), the first time a particle leaves a site x it departs east; the next time this or another particle leaves x it departs south; the next departure is west, then north, then east again, etc. More generally, in any dimension d ≥ 1, for each site x ∈ Z fix a cyclic ordering of its 2d neighbors, and requi...
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2012
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2012.v3.n2.a3