Course Archives Theoretical Statistics and Mathematics Unit

Course: Topics in Discrete Probability Instructor: Yogeshwaran D Room: G23 Level: Postgraduate Time: Currently offered

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 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. Evaluation: Midterm Exam 15 marks Assignment 35 marks Final Exam 50 marks Total 100 marks Top of the page Past Exams

Midterm 23.pdf 25.pdf Semestral 23.pdf Supplementary and Back Paper 23.pdf Top of the page

[ Semester Schedule ][ SMU ] [Indian Statistical Institute]