Discrete Probability (MA40239)

Semester II 2017-18

Lecturers

Mathew Penrose and Florian Völlering

Content:

Random Graphs: definition and motivation; small subgraphs; giant component and phase transition; maximum degree; clique number. Other aspects of random graphs such as: connectivity, chromatic number, bipartite matchings, sharp thresholds. Percolation Theory: non-triviality of the phase transition; lattice animals, percolation on trees, uniqueness of the infinite component, properties and interpretation of the percolation probability. Other aspects of percolation theory such as: the critical value on the square lattice, self-avoiding walk, random resistor networks. Further topics in discrete probability may be considered such as: invariant distributions, bounds and cut-off phenomena for Markov chain mixing times and examples thereof; entropy, noiseless coding, discrete memoryless channel in information theory.

Books

News

Lecture notes.

Problem sheets

Solutions to problem sheets