CEU Electronic Theses and Dissertations, 2021
| Author | Meszaros, Andras |
|---|---|
| Title | Graph convergence, determinantal processes and the sandpile group of random regular graphs |
| Summary | First, we study the distribution of the sandpile group of random d-regular graphs. For the directed model, we prove that it follows the Cohen-Lenstra heuristics, that is, the limiting probability that the p-Sylow subgroup of the sandpile group is a given p-group P, is proportional to |Aut(P)|^-1. Similar results hold for undirected random regular graphs, where for odd primes the limiting distributions are the ones given by Clancy, Leake and Payne. Then, we extend Lyons’s tree entropy theorem to general determinantal measures. |
| Supervisor | Abert, Miklos |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2021/meszaros_andras.pdf |
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