Large Boltzmann planar maps with a stable exponent alpha converge in the Gromov-Hausdorff-Prokhorov sense to an explicit random compact metric space S_alpha of Hausdorff dimension 2 alpha.
Some properties of stable snakes
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abstract
We prove some technical results relating to the Brownian snake on a stable L\'evy tree. This includes some estimates on the range of the snake, estimates on its occupation measure around its minimum and also a proof of the fact that the snake and the height function of the associated tree have no common increase points.
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The scaling limit of planar maps with large faces
Large Boltzmann planar maps with a stable exponent alpha converge in the Gromov-Hausdorff-Prokhorov sense to an explicit random compact metric space S_alpha of Hausdorff dimension 2 alpha.