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Local structure of random quadrangulations

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arxiv math/0512304 v2 pith:QOWRJSDF submitted 2005-12-14 math.PR

classification math.PR
keywords quadrangulationslocalbranchingcertainprocessrandomadaptationbiparametric
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This paper is an adaptation of a method used in \cite{K} to the model of random quadrangulations. We prove local weak convergence of uniform measures on quadrangulations and show that the local growth of quadrangulation is governed by certain critical time-reversed branching process and the rescaled profile converges to the reversed continuous-state branching process. As an intermediate result we derieve a biparametric generating function for certain class of quadrangulations with boundary.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  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).

  2. Characterisation of Markov property on planar maps

    math.PR 2025-05 conditional novelty 7.0 of 10

    The only rerooting-invariant Markovian random quadrangulations are Boltzmann maps, and every submap that induces a Markovian decomposition is a 'stopping map,' a class strictly larger than peeling explorations.

  3. First-passage percolation in random planar maps and Tutte's bijection

    math.PR 2019-06 unverdicted novelty 6.0 of 10

    FPP distance in random quadrangulations and planar maps scales asymptotically as a constant times graph distance; Tutte bijection preserves this equivalence at large scales.

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