Deterministic Random Walks on the Integers

Details Deterministic Random Walks on the Integers Deterministic Random Walks on the Integers

2006-02-14

arxiv.org/abs/math/0602300v1

Mathematics

Combinatorics

27 pages, 0 figured

Scientific paper

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 c_1, which is approximately 2.29. For intervals of length L, this improves to a difference of O(log L), for the L_2 average of a contiguous set of intervals even to O(sqrt{log L}). All these bounds are tight.

Affiliated with

Also associated with

No associations

Rating

Deterministic Random Walks on the Integers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Deterministic Random Walks on the Integers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deterministic Random Walks on the Integers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-568347