Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile

Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality: an explanation of the 1/f noise. Phys. Rev. Lett. 59(4), 381–384 (1987)

Cook, M.: The tent metaphor. http://paradise.caltech.edu/~cook/Warehouse/ForPropp/ (2002)

Cooper, J.N., Spencer, J.: Simulating a random walk with constant error. Combin. Probab. Comput. 15, 815–822 (2006). http://www.arxiv.org/abs/math.CO/0402323

Diaconis, P., Fulton, W.: A growth model, a game, an algebra, Lagrange inversion, and characteristic classes. Rend. Sem. Mat. Univ. Politec. Torino 49(1), 95–119 (1991)

Fey, A., Redig, F.: Limiting shapes for deterministic centrally seeded growth models. J. Statist. Phys. 130(3), 579–597 (2008). http://arxiv.org/abs/math.PR/0702450

Fukai, Y., Uchiyama, K.: Potential kernel for two-dimensional random walk. Ann. Probab. 24(4), 1979–1992 (1996)

Kleber, M.: Goldbug variations. Math. Intelligencer 27(1), 55–63 (2005)

Koosis, P.: La plus petite majorante surharmonique et son rapport avec l’existence des fonctions entières de type exponentiel jouant le rôle de multiplicateurs. Ann. Inst. Fourier (Grenoble) 33 fasc. (1), 67–107 (1983)

Lawler, G.: Intersections of Random Walks. Birkhäuser, Boston (1996)

Lawler, G., Bramson, M., Griffeath, D.: Internal diffusion limited aggregation. Ann. Probab. 20(4), 2117–2140 (1992)

Lawler, G.: Subdiffusive fluctuations for internal diffusion limited aggregation. Ann. Probab. 23(1), 71–86 (1995)

Le Borgne, Y., Rossin, D.: On the identity of the sandpile group. Discrete Math. 256, 775–790 (2002)

Levine, L.: The rotor-router model. Harvard University senior thesis. http://arxiv.org/abs/math/0409407 (2002)

Levine, L., Peres, Y.: Spherical asymptotics for the rotor-router model in $\mathbb{Z}^d$. Indiana Univ. Math. J. 57(1), 431–450 (2008). http://arxiv.org/abs/math/0503251

Levine, L., Peres, Y.: The rotor-router shape is spherical. Math. Intelligencer 27(3), 9–11 (2005)

Levine, L., Peres, Y.: Scaling limits for internal aggregation models with multiple sources. http://arxiv.org/abs/0712.3378 (2007)

Lindvall, T.: Lectures on the Coupling Method. Wiley, New York (1992)

Priezzhev, V.B., Dhar, D., Dhar, A., Krishnamurthy, S.: Eulerian walkers as a model of self-organised criticality. Phys. Rev. Lett. 77, 5079–82 (1996)

Propp, J.: Three lectures on quasirandomness. http://faculty.uml.edu/jpropp/berkeley.html (2004)

Spitzer, F.: Principles of Random Walk. Springer, New York (1976)

Uchiyama, K.: Green’s functions for random walks on $\mathbb{Z}^N$. Proc. London Math. Soc. 77(1), 215–240 (1998)

Van den Heuvel, J.: Algorithmic aspects of a chip-firing game. Combin. Probab. Comput. 10(6), 505–529 (2001)