CEU Electronic Theses and Dissertations, 2020
| Author | Hrušková, Aranka |
|---|---|
| Title | Random graphs with finite expected degree and Local algorithms on lattices |
| Summary | In the first part of the thesis, motivated by the recent paper by Backhausz and Szegedy which unifies and generalises the concepts of dense (graphon) and local-global (graphing) convergence, we prove a number of inequalities relating the degree sequence of a graph and the operator norms of its adjacency matrix. We then use these to explore the properties of the Erdős-Rényi model G(n, c/(n−1)), in which for each vertex its expected degree is a constant c independent of n. The second part of the thesis constructs factor of iid algorithms for obtaining balanced orientation of the triangular lattice and of the square grid. |
| Supervisor | Kunszenti-Kovács, David |
| Department | Mathematics Ps |
| Full text | https://www.etd.ceu.edu/2020/hruskova_aranka.pdf |
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