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Pattern occurrences in random planar maps

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arxiv 1801.10007 v2 pith:MH7TCBCA submitted 2018-01-30 math.CO math.PR

Michael Drmota , Benedikt Stufler This is my paper · ORCID
classification math.COmath.PR
keywords mapsnumberoccurrencespatternplanaradjustedasymptoticallyboltzmann
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We consider planar maps adjusted with a (regular critical) Boltzmann distribution and show that the expected number of pattern occurrences of a given map is asymptotically linear when the number n of edges goes to infinity. The main ingredient for the proof is an extension of a formula by Liskovets (1999).

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  1. Local convergence of random planar graphs

    math.PR 2019-08 conditional novelty 8.0 of 10

    Uniform connected planar graphs have a quenched local limit, a new infinite random graph called the uniform infinite planar graph (UIPG).

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