Stufler, Benedikt (2015): Scaling limits of random trees and graphs. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics |

Preview |
PDF
Stufler_Benedikt.pdf 1MB |

**DOI**: 10.5282/edoc.18812

### Abstract

In this thesis, we establish the scaling limit of several models of random trees and graphs, enlarging and completing the now long list of random structures that admit David Aldous' continuum random tree (CRT) as scaling limit. Our results answer important open questions, in particular the conjecture by Aldous for the scaling limit of random unlabelled unrooted trees. We also show that random graphs from subcritical graph classes admit the CRT as scaling limit, proving (in a strong from) a conjecture by Marc Noy and Michael Drmota, who conjectured a limit for the diameter of these graphs. Furthermore, we provide a new proof for results by Bénédicte Haas and Grégory Miermont regarding the scaling limits of random Pólya trees, extending their result to random Pólya trees with arbitrary vertex-degree restrictions.

Item Type: | Theses (Dissertation, LMU Munich) |
---|---|

Keywords: | continuum random tree, scaling limits, random trees, random graphs, invariance principles |

Subjects: | 500 Natural sciences and mathematics 500 Natural sciences and mathematics > 510 Mathematics |

Faculties: | Faculty of Mathematics, Computer Science and Statistics |

Language: | English |

Date of oral examination: | 23. October 2015 |

1. Referee: | Panagiotou, Konstantinos |

MD5 Checksum of the PDF-file: | 879cfbe7fa52941027ad0f80d36461bb |

Signature of the printed copy: | 0001/UMC 23313 |

ID Code: | 18812 |

Deposited On: | 03. Nov 2015 09:41 |

Last Modified: | 23. Oct 2020 21:30 |