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Scaling constants and the lazy peeling of infinite Boltzmann planar maps

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Random Geometry

Recently Curien and Le Gall derived precise scaling limits of the volume and perimeter of the explored region during a (“simple”) peeling process of uniform infinite planar triangulations (UIPT) and quadrangulations (UIPQ). We show that the same limits may be obtained for a slightly modified “lazy” peeling process in the more general setting of infinite Boltzmann planar maps (IBPM) with arbitrary (regular critical) weight sequences. Combining the scaling constants involved with previous results by Miermont on graph distances in Boltzmann planar maps, we show how one may obtain (at least at a heuristic level) simple expressions for all constants appearing in the relative scaling of the following quantities associated to an IBPM : volume, perimeter, graph distance, dual graph distance, first-passage time, and hop count. Finally we will comment on how one may recover the simple peeling process from the lazy one.

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

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