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We prove that random triangulations of types I, II, and III with a simple boundary under the critical Boltzmann weight converge in the scaling limit to the Brownian disk.
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by same author, The topological structure of scaling limits of large planar maps , Invent. Math. 169
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L. Addario-Berry and M. Albenque, The scaling limit of random simple triangulations and random simple quadrangulations , Ann. Probab. 45
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J. Bettinelli and G. Miermont, Compact Brownian surfaces I. Brownian disks , Probab. Theory Related Fields 167
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2010
Cited alongside, same era.
J. Beltran and J.-F. Le Gall, Quadrangulations with no pendant vertices , Bernoulli 19
2013
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by same author, Uniqueness and universality of the Brownian map , Ann. Probab. 41
2013
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G. Miermont, The Brownian map is the scaling limit of uniform random plane quadrangulations , Acta Math. 210
2013
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J. Bettinelli, E. Jacob, and G. Miermont, The scaling limit of uniform random plane maps, via the Ambjørn-Budd bijection , Electron. J. Probab. 19
2014
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S. Janson, Tail bounds for sums of geometric and exponential variables , Technical report (2014)
2014
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M. Albenque and D. Poulalhon, A generic method for bijections between blossoming trees and planar maps , The Electronic Journal of Combinatorics 22
2015
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2018
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J. Bertoin, N. Curien, and I. Kortchemski, Random planar maps and growth-fragmentations , Ann. Probab. 46
2018
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2019
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2019
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by same author, Convergence of the free Boltzmann quadrangulation with simple boundary to the Brownian disk , Ann. Inst. Henri Poincaré Probab. Stat. 55
2019
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2019
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by same author, Brownian disks and the Brownian snake , Ann. Inst. Henri Poincaré Probab. Stat. 55
2019
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