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On the maximal offspring in a subcritical branching process

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arxiv 1901.04603 v2 pith:47GRGPRH submitted 2019-01-14 math.PR

Benedikt Stufler This is my paper · ORCID
classification math.PR
keywords maximaloffspringsubcriticalassumptionsbranchingconditionedconsiderfixed
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abstract

We consider a subcritical Galton--Watson tree conditioned on having $n$ vertices with outdegree in a fixed set $\Omega$. Under mild regularity assumptions we prove various limits related to the maximal offspring of a vertex as $n$ tends to infinity.

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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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