Belle, Thomas van (2020) Uniqueness of the infinite open cluster on the stationary distributions of interacting particle systems. Master's Thesis / Essay, Mathematics.
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Abstract
In classical percolation models the sites (or bonds) are declared open independently with a parameter p. The stationary distributions of interacting particle systems give a correlated field of 0’s and 1’s on Z d , which can be used to determine open and closed sites. The resulting percolation models have a long-range dependence. In this thesis we consider the stationary distributions of the voter model and the contact process. For both percolation models, it will be shown that the infinite open connected component is almost surely unique.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Rodrigues Valesin, D. and Muller, T. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 15 Jan 2021 08:50 |
| Last Modified: | 23 Jul 2021 10:55 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/23642 |
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