401-3604-66L Special Topics in Probability: Recent Developments in Percolation Theory
Semester | Autumn Semester 2016 |
Lecturers | P. Nolin |
Periodicity | non-recurring course |
Language of instruction | English |
Abstract | The goal of this course is to present recent developments in Percolation Theory |
Objective | The goal of this course is to present recent developments in Percolation Theory |
Content | Independent percolation is obtained by deleting randomly (and independently) the edges of a lattice, each with a given probability p between 0 and 1. One is then interested in the connectivity properties of the random subgraph so-obtained. It is arguably the simplest model from statistical mechanics that displays a phase transition, a drastic change of behavior as the parameter p varies. We will first present classical tools and properties of percolation theory: in particular correlation inequalities, exponential decay of connection probabilities, and uniqueness of the infinite connected component. We will then discuss recent developments: for example percolation on Cayley graphs, and continuum limits in two dimensions. |
Literature | B. Bollobas, O. Riordan: Percolation, CUP 2006 G. Grimmett: Percolation 2ed, Springer 1999 |
Prerequisites / Notice | Prerequisites: 401-2604-00L Probability and Statistics (mandatory) 401-3601-00L Probability Theory (recommended) |