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Thesis - Master's thesis | @MastersThesis | Masterarbeit

Author(s)*:Friedrich, Tobias
BibTeX citekey*:Friedrich2005

Title, School
Title*:Deterministic Random Walks on Infinite Grids
School:Friedrich-Schiller-Universität Jena
Type of Thesis*:Master's thesis

Note, Abstract, Copyright
Note:Mathematik-Diplomarbeit, eingereicht an der Friedrich-Schiller-Universität Jena
LaTeX Abstract: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 $7.7\Delta < c' < 26.9\Delta$.

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Referees, Status, Dates
Date Kolloquium:1 April 2006

MPG Unit:Max-Planck-Institut für Informatik
MPG Subunit:Algorithms and Complexity Group
MPG Subsubunit:Discrete Math Group
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BibTeX Entry:
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},

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Entry last modified by Christine Kiesel, 04/20/2006
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Tobias Friedrich
04/01/2006 03:12:26 PM

Christine Kiesel
Tobias Friedrich

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