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Pattern occurrences in random planar maps

· 2018 · math.CO · arXiv 1801.10007

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abstract

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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math.PR 1

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2019 1

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CONDITIONAL 1

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Local convergence of random planar graphs

math.PR · 2019-08-13 · conditional · novelty 8.0

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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  • Local convergence of random planar graphs math.PR · 2019-08-13 · conditional · none · ref 26 · internal anchor

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