منابع مشابه
The 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 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.
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...
متن کاملInterpolating between random walk and rotor walk
We introduce a family of stochastic processes on the integers, depending on a parameter p ∈ [0, 1] and interpolating between the deterministic rotor walk (p = 0) and the simple random walk (p = 1/2). This p-rotor walk is not a Markov chain but it has a local Markov property: for each x ∈ Z the sequence of successive exits from x is a Markov chain. The main result of this paper identifies the sc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Statistical Mechanics: Theory and Experiment
سال: 2016
ISSN: 1742-5468
DOI: 10.1088/1742-5468/2016/04/043207