Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
Course: Topics in Discrete Probability Instructor: Siva Athreya Room: G25 Level: Postgraduate Time: Currently offered |
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Syllabus Past Exams Syllabus: i) Review of discrete probability, First and Second Moment methods, Chernoff bounds and some applications. ii) Percolation on lattices: Phase-transition phenomena, subcritical and supercriti- cal phases, Uniqueness. iii) Random graphs: Phase transition, Influences, Russo’s formula and Sharp thresh- olds. 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. Evaluation:
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