Critical values in continuum and dependent percolation

Abstract

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.

Date of Award	1 Jun 2011
Original language	English
Awarding Institution	University of Bath
Supervisor	Mathew Penrose (Supervisor)