Course Archives Theoretical Statistics and Mathematics Unit

Course: Topics in Discrete Probability Time: Currently not offered Level: Postgraduate

Syllabus 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. Top of the page Past Exams

Midterm 19.pdf Semestral 19.pdf Supplementary and Back Paper Top of the page

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