Random Graphs

Code: MA686 | L-T-P-C: 3-0-0-6

Prerequisites: MA225 or MA590

Probabilistic tools for random graphs: Convergence of random variables, probabilistic bounds, coupling, martingales; Branching processes: Survival vs extinction, random walk perspective, binomial and Poisson branching processes; Erdos-Renvi random graphs: Comparison to branching processes, phase transition for the largest connected component, central limit theorem for the giant component, behavior in the critical window, degree structure; Random graph models for complex networks: Degree structure, connectivity properties, small world behavior.

Text:

1. R. V. D. Hofstad, Random Graphs and Complex Networks, Volume 1, Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, 2017.
2. R. Durrett, Random Graph Dynamics, Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, 2007.

References:

1. B. Bollobas Random Graphs, Second edition, Cambridge studies in advanced mathematics, Cambridge University Press, 2001