Javascript must be enabled for the correct page display

A sharp threshold for an anisotropic bootstrap percolation model

Boerma, S. (2014) A sharp threshold for an anisotropic bootstrap percolation model. Bachelor's Thesis, Mathematics.

[img]
Preview
Text
Bachelorverslag-susan-boerma.pdf - Published Version

Download (166kB) | Preview
[img] Text
BoermaAkkoordVanEnter.pdf - Other
Restricted to Repository staff only

Download (30kB)

Abstract

In bootstrap percolation on the two-dimensional lattice the initial state of any site is infected with probability p and healthy with prob- ability 1 − p. A healthy site can become infected if its neighbors are and an infected site remains infected for all time. The process goes on until all sites are infected or there is a point where no more sites can become infected. If all the sites become infected we say the initial configuration percolates. Balogh and Bollobs [BB03] were able to give a sharp threshold for the standard bootstrap percolation model in a way that can be used for other models. In this bachelor thesis a sharp threshold is given for the anisotropic bootstrap percolation model. The standard and the anisotropic model are compared and it is shown that the fundamental theorem of Friedgut and Kalai [FK96] can be used to give the sharp threshold in both cases. It is shown that the behaviour on the grid and the torus is almost the same. Using a slightly adjusted version of the lemma of Aizenman and Lebowitz [AL88], the length of the epsilon-window for anisotropic bootstrap percolation is determined.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 07:56
Last Modified: 15 Feb 2018 07:56
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/11617

Actions (login required)

View Item View Item