In the first part of this thesis I consider site and bond percolation on a Random Connection Model and prove that for a wide range of connection functions the critical site probability is strictly greater than the critical bond probability and use this fact to improve previously known non-strict inequalities to strict inequalities. In the second part I consider percolation on the even phase of a Random Sequential Adsorption model and prove that the critical intensity is finite and strictly bigger than 1. Both of these main results make use of an enhancement technique.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:545313 |
| Date | January 2011 |
| Creators | Rosoman, Thomas |
| Contributors | Penrose, Mathew |
| Publisher | University of Bath |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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