University of Groningen
Inhomogeneous contact process and percolation
Szabó, Réka
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Publication date: 2019
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Szabó, R. (2019). Inhomogeneous contact process and percolation. Rijksuniversiteit Groningen.
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Propositions accompanying the PhD thesis
Inhomogeneous contact process and percolation R´eka Szab´o
1. The behavior of random processes can be significantly af-fected by the introduction of inhomogeneities in the envi-ronment.
2. There exists a tree on which the contact process survives for any positive infection parameter but, if a certain edge is removed, one obtains two subtrees on which the contact process dies out for small parameters. (Chapter 1)
3. If the percolation parameter is simultaneously changed on finitely many fixed infinite columns of the ladder graph de-fined in Chapter 2, the critical parameter changes as a con-tinuous function. (Chapter 2)
4. An oriented graph can be defined in analogy with the non-oriented ladder graph, and similar results can be obtained for the inhomogeneous percolation model, as described in Proposition 3. (Chapter 2)
5. Consider an oriented d-regular tree with additional edges of length k pointing from each vertex to its descendants k generations below. The critical curve of the inhomogeneous percolation model of Chapter 3 on this graph is strictly above the line dp + dkq = 1. (Chapter 3)
6. The above-mentioned percolation model can be described as a multi-type branching process. (Chapter 3)
7. In analogy with multi-type branching processes limit the-orems can be stated for the subcritical, critical and super-critical phases of the percolation model. (Chapter 3)
