Chip-firing and rotor-routing on directed graphs. (English) Zbl 1173.82339

Holroyd, Alexander E.; Levine, Lionel; Mészáros, Karola; Peres, Yuval; Propp, James; Wilson, David B.

Sidoravicius, Vladas (ed.) et al., In and out of equilibrium 2. Papers celebrating the 10th edition of the Brazilian school of probability (EBP), Rio de Janiero, Brazil, July 30 to August 4, 2006. Basel: Birkhäuser (ISBN 978-3-7643-8785-3/hbk). Progress in Probability 60, 331-364 (2008).

Summary: We give a rigorous and self-contained survey of the abelian sandpile model and rotor-router model on finite directed graphs, highlighting the connections between them. We present several intriguing open problems.
For the entire collection see [Zbl 1141.82002].

MSC:

82C20	Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
20K01	Finite abelian groups
05C25	Graphs and abstract algebra (groups, rings, fields, etc.)

Keywords:

abelian sandpile model; rotor-router model; chip firing; Eulerian walkers