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


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

Suggested Texts :
(a) C. Garban and J. Steif: Noise Sensitivity of Boolean Functions and Percolation.
(b) N. Lanchier: Stochastic Modelling.
(c) Sebastien Roch: Modern Discrete Probability: A toolkit. (Notes).
(d) R. Lyons and Y. Peres: Probability on trees and networks.
(e) M. Barlow: Random walks and heat kernel on Graphs.

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Past Exams
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