Course Archives Theoretical Statistics and Mathematics Unit
Course: Topics in Discrete Probability
Time: Currently not offered
Level: Postgraduate
Past Exams

Syllabus: Review of discrete probability, First and Second Moment methods, Chernoff bounds and some applications. Percolation on lattices : Phase-tranition phenomena, subcritical and supercritical phases, Uniqueness. Random graphs : Phase transition, Influences, Russo's formula and Sharp thresholds. Noise Sensitivity and Stability. Introduction to Markov chains and Martingales. Branching processes. Random walks and electrical networks, Uniform spanning trees.

Suggested Texts :

1. C. Garban and J. Steif : Noise Sensitivity of Boolean Functions and Percolation.
2. N. Lanchier : Stochastic Modelling.
3. Sebastien Roch : Modern Discrete Probability : A toolkit. (Notes).
4. R. Lyons and Y. Peres : Probability on trees and networks.
5. M. Barlow : Random walks and heat kernel on Graphs.

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Past Exams


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