The Rotor-Router Model

  title={The Rotor-Router Model},
  author={Lionel Levine},
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 invariant of this dynamical system yields links between the behavior of the system and diophantine… CONTINUE READING
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A growth model, a game, an algebra, Lagrange inversion, and characteristic classes

  • P. Diaconis, W. Fulton
  • Rend. Sem. Mat. Univ. Pol. Torino 49 (1991), no…
  • 1991
Highly Influential
4 Excerpts

Sturmian words

  • J. Berstel, P. Seebold
  • Algebraic Combinatorics on Words, M. Lothaire, ed…
  • 2002
2 Excerpts

Subdiffusive fluctuations for internal diffusion-limited aggregation

  • G. F. Lawler
  • Annals of Probability 23 (1995), no. 1, 71–86.
  • 1995
1 Excerpt

Fractals and diffusion-limited aggregation

  • Barlow, T M.
  • Bull. Sci. Math 117 (1993), no. 1, 161–169.
  • 1993
1 Excerpt

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