Abstract
Many random recursive discrete structures may be described by a single generic model. Adopting this perspective allows us to elegantly prove limits for these structures as instances of general underlying principles, and describe their phase diagrams using a unified terminology. We illustrate this by a selection of examples. We consider random outer-planar maps sampled according to arbitrary weights assigned to their inner faces, and classify in complete generality distributional limits for both the asymptotic local behaviour near the root-edge and near a uniformly at random drawn vertex. We consider random connected graphs drawn according to weights assigned to their blocks and establish a local weak limit. We also apply our framework to recover in a probabilistic way a central limit theorem for the size of the largest 2-connected component in random graphs from planar-like classes. We prove local convergence of random k-dimensional trees and establish both scaling limits and local weak limits for random planar maps drawn according to Boltzmann-weights assigned to their 2-connected components.
Dokumententyp: | Zeitschriftenartikel |
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Fakultät: | Mathematik, Informatik und Statistik > Mathematik |
Themengebiete: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
ISSN: | 1549-5787 |
Sprache: | Englisch |
Dokumenten ID: | 88964 |
Datum der Veröffentlichung auf Open Access LMU: | 25. Jan. 2022, 09:28 |
Letzte Änderungen: | 25. Jan. 2022, 09:28 |