Scaling limits of random trees and graphs

Stufler, Benedikt (2015): Scaling limits of random trees and graphs. Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik

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.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Keywords: continuum random tree, scaling limits, random trees, random graphs, invariance principles
• Themengebiete: 500 Naturwissenschaften und Mathematik ; 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Fakultäten: Fakultät für Mathematik, Informatik und Statistik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 23. Oktober 2015
• 1. Bericht­erstatter:in: Panagiotou, Konstantinos