| Course Archives Theoretical Statistics and Mathematics Unit | ||
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Course: Special Topic 1: Random Graphs and Limits Time: Currently not offered Level: Postgraduate |
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| Syllabus
Past Exams Syllabus: The course will aim to introduce basics of random graphs and illustrate via applications two types of graph limits - sparse graph limits (local weak convergence) and dense graph limits. Galton-Watson trees- Extinction probability and other basic properties. Erdos-Renyi random graphs - Subgraph counts, Cycle counts and Poisson approximation. Local weak convergence - Converging graph sequences. Basic examples. Convergence of Erdos-Renyi graphs. Applications to subtree counts and phase transition. Dense Graphs, Graph limits and Graphons. Pre-Requisites: Probability I and II at B.Math level. Measure-theoretic probability. Recommended to attend Advanced Probability course in parallel. Suggested Texts : 1. Sebastien Roch : Modern Discrete Probability : A toolkit. (Notes online). 2. G. Grimmett : Probability on Graphs. 3. Random Graphs - Svante Janson, Tomasz Luczak, Andrzej Rucinski. 4. Lecture notes on random graphs and probabilistic combinatorial optimization - Charles Bordenave (Notes online). 5. Random Graphs and Complex Networks - Remco Van Der Hofstad (Notes online). 6. Large Networks and Graph Limits - Laszlo Lovasz (American Mathematical Society). Top of the page Past Exams | ||
Midterm
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