Criticality in the Abelian sandpile model

Bachelor thesis (2021)

Authors

B.T. van Tol Applied Sciences

Contributors

F.H.J. Redig Applied Probability - EEMCS (mentor)
J.M. Thijssen QN/Thijssen Group - AS (mentor)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2021 Berend van Tol
More Info
expand_more

Published Date

26-08-2021

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In this thesis we study criticality in the context of the dissipative Abelian sandpile model. The model is linked to a simple trapped random walk, giving a practical method to determine criticality for certain landscapes of dissipative sites. The main results concern the lifetime of the random walk, especially the divergence of its first moment for traps placed on spherical shells. For the one dimensional case the point of divergence is determined with reasonable precision. In higher dimensions the divergence is shown to be possible for an infite amount of shells. The connection between the sandpile model and a random walk is shown mathematically and further researched via simulation.