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EJC
2007

Deterministic random walks on the integers

13 years 3 months ago
Deterministic random walks on the integers
Jim Propp’s P-machine, also known as the ‘rotor router model’ is a simple deterministic process that simulates a random walk on a graph. Instead of distributing chips to randomly chosen neighbors, it serves the neighbors in a fixed order. We investigate how well this process simulates a random walk. For the graph being the infinite path, we show that, independent of the starting configuration, at each time and on each vertex, the number of chips on this vertex deviates from the expected number of chips in the random walk model by at most a constant c1, which is approximately 2.29. For intervals of length L, this improves to a difference of O(log L), for the L2 average of a contiguous set of intervals even to O( √ log L). All these bounds are tight. 1 The Propp Machine The following deterministic process was suggested by Jim Propp as an attempt to derandomize random walks on infinite grids Zd: ∗ The authors enjoyed the hospitality, generosity and the strong coffee of th...
Joshua N. Cooper, Benjamin Doerr, Joel H. Spencer,
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where EJC
Authors Joshua N. Cooper, Benjamin Doerr, Joel H. Spencer, Gábor Tardos
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