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

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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 vertexdegree restrictions.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  continuum random tree, scaling limits, random trees, random graphs, invariance principles 
Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 510 Mathematics 
Faculties:  Faculty of Mathematics, Computer Science and Statistics 
Language:  English 
Date Accepted:  23. October 2015 
1. Referee:  Panagiotou, Konstantinos 
Persistent Identifier (URN):  urn:nbn:de:bvb:19188120 
MD5 Checksum of the PDFfile:  879cfbe7fa52941027ad0f80d36461bb 
Signature of the printed copy:  0001/UMC 23313 
ID Code:  18812 
Deposited On:  03. Nov 2015 09:41 
Last Modified:  03. Nov 2015 09:41 