Geodesic
Deterministic Random Walks on the Integers
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005).

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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. 
@article{DMTCS_2005_special_250_a45,
     author = {Cooper, Joshua and Doerr, Benjamin and Spencer, Joel and Tardos, G\'abor},
     title = {Deterministic {Random} {Walks} on the {Integers}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)},
     year = {2005},
     doi = {10.46298/dmtcs.3436},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3436/}
}
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AU  - Doerr, Benjamin
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AU  - Tardos, Gábor
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%0 Journal Article
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%A Doerr, Benjamin
%A Spencer, Joel
%A Tardos, Gábor
%T Deterministic Random Walks on the Integers
%J Discrete mathematics & theoretical computer science
%D 2005
%V DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
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%F DMTCS_2005_special_250_a45
Cooper, Joshua; Doerr, Benjamin; Spencer, Joel; Tardos, Gábor. Deterministic Random Walks on the Integers. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005). doi : 10.46298/dmtcs.3436. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3436/

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