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Master's thesis | @MastersThesis{Friedrich2005, ... | Masterarbeit

Friedrich, Tobias

Deterministic Random Walks on Infinite Grids

Friedrich-Schiller-Universität Jena, December, 2005

Mathematik-Diplomarbeit, eingereicht an der Friedrich-Schiller-Universität Jena


The rotor-router model is a simple deterministic analogue of random walk invented by Jim Propp. Instead of distributing chips to randomly chosen neighbors, it serves the neighbors in a fixed order. This thesis investigates how well this process simulates
a random walk on an infinite two-dimensional grid. 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 $c$. It is proved that $7.2 < c < 11.8$ in general. Surprisingly, these bounds depend on the order in which the neighbors are served. It is also shown that in a generalized setting, where one just requires that no neighbor gets more than
$\Delta$ chips more than another, there is also such a constant $c'$ with $7.7\Delta < c' < 26.9\Delta$.
www.mpi-inf.mpg.de/~tfried/Propp/
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April
2006
Max-Planck-Institut für Informatik
Algorithms and Complexity Group
Discrete Math Group
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BibTeX Entry:
@MASTERSTHESIS{Friedrich2005,
AUTHOR = {Friedrich, Tobias},
TITLE = {Deterministic Random Walks on Infinite Grids},
SCHOOL = {Friedrich-Schiller-Universit{\"a}t Jena},
YEAR = {2005},
TYPE = {Master's thesis}
MONTH = {December},
NOTE = {Mathematik-Diplomarbeit, eingereicht an der Friedrich-Schiller-Universität Jena},
}





Entry last modified by Christine Kiesel, 04/20/2006
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Editor(s)
Tobias Friedrich
Created
04/01/2006 03:12:26 PM
Revision
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Editor
Christine Kiesel
Tobias Friedrich


Edit Date
20.04.2006 18:18:47
01.04.2006 15:12:26