The Random Geometric Graphs reading course meets MWF from 10-12 in APM 6218. Our primary reference is Random Geometric Graphs by Mathew Penrose. For each meeting we have one person assigned to present that day's reading.

Schedule

Date    Presenter    Material
June 22    Franklin Kenter    Penrose, sections 2.1-2.3: Probabilistic tools: Poisson and normal approximations
June 24    Mary Radcliffe    Penrose, sections 2.4-2.6: Probabilistic tools: Martingales and De-Poissonization
June 26    Andy Parrish    Penrose, sections 3.1-3.3: Subgraph and component counts: expectations, Poisson approximation, and second moments
June 29    Alex Eustis    Penrose, sections 3.4-3.7: Subgraph and component counts: normal approximations and strong laws of large numbers
July 1    Jake Hughes    Giant Component and Connectivity in Geographical Threshold Graphs, by Bradonjic, Hagberg, and Percus
July 3    Franklin Kenter    Penrose, sections 4.1-4.3: Typical vertex degrees, laws of large numbers, asymptotic covariances
July 6    Alex Eustis    Penrose, sections 4.4-4.5: Typical vertex degrees, moments for de-Poissonization, central limit theorems
July 8    Mary Radcliffe    Hamiltonicity of the Random Geometric Graph, by Krivelevich and Muller
July 10    Andy Parrish    Penrose 9.1-9.3: Percolation tools
July 13    Andy Parrish    Penrose 9.3: [continued]
July 15    Jake Hughes    Penrose 9.4-9.5: More percolation, and ergodic theory
July 17    Franklin Kenter    Results from "Random Heterogeneous Materials" by Torquato
July 20    Alex Eustis    Penrose 10.1, 10.2: The largest component of an RGG
July 22    Fan Chung Graham    Research problems
July 24    Andy Parrish    Penrose 10.3: Uniqueness of the giant component
July 27    Jake Hughes    Zhennig Kong and Edmund Yeh: Connectivity and Information Dissemination in Large-Scale Wireless Networks with Dynamic Links
July 29    Free-for-all    Deciding who will work on which research problems

Problems to explore