Topics in Discrete Probability

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.

https://www.isibang.ac.in/~adean/infsys/database/MMath/E19TDP.html