Graph limits of random unlabelled k-trees

2018/01/30 by Emma Yu Jin, Benedikt Stufler, Jin, Emma Yu +1
Computer Science · Mathematics · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis #math.CO #math.PR #msc:60C05

paper · pdf · doi:10.48550/arxiv.1801.10097

arxiv created 2018/01/30 · arxiv updated 2018/01/31

Abstract

We study random unlabelled k-dimensional trees by combining the colouring approach by Gainer-Dewar and Gessel (2014) with the cycle pointing method by Bodirsky, Fusy, Kang and Vigerske (2011). Our main applications are Gromov-Hausdorff-Prokhorov and Benjamini-Schramm limits, that describe their asymptotic geometric shape on a global and local scale as the number of hedra tends to infinity.

Citations

• Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen

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