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Scaling limits of random planar maps and growth-fragmentations

Friday 24th April 2015 - 15:30 to 16:30
INI Seminar Room 1
Co-authors: Jean Bertoin (University Zürich), Igor Kortchemski (CNRS and École Polytechnique)

We prove a scaling limit result for the structure of cycles at heights in random Boltzmann triangulations with a boundary. The limit process is described as a compensated fragmentation process of index $-1/2$ with explicit parameters. The proof is based on the analysis of the peeling by layers algorithm in random triangulations. However, contrary to previous works on the subject we let the exploration branch and explore different components. The analysis heavily relies on a martingale structure inside random planar triangulations and a recent scaling limits result for discrete time Markov chains. One motivation is to give a new construction of the Brownian map from a compensated growth-fragmentation process.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons