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Deterministic Random Walks on the Integers

Abstract : 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.
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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. ⟨hal-01184393⟩

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