Deterministic Random Walks on the Integers

Joshua Cooper (1) , Benjamin Doerr (2) , Joel Spencer (1) , Gábor Tardos (3)

1 CIMS - Courant Institute of Mathematical Sciences [New York]
2 MPII - Max-Planck-Institut für Informatik
3 Alfréd Rényi Institute of Mathematics

We analyze the one-dimensional version of Jim Propp's $P$-machine, a simple deterministic process that simulates a random walk on $\mathbb{Z}$. The "output'' of the machine is astonishingly close to the expected behavior of a random walk, even on long intervals of space and time.

Mots clés: random walks; chip firing games.

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Joshua Cooper, Benjamin Doerr, Joel Spencer, Gábor Tardos. Deterministic Random Walks on the Integers. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.73-76, ⟨10.46298/dmtcs.3436⟩. ⟨hal-01184393⟩