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Scaling limits of random planar maps and growth-fragmentations

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Random Geometry

Co-authors: Jean Bertoin (University Zrich), Igor Kortchemski (CNRS and cole 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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