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.
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 |