The scaling limits of uniform connected graphs with fixed surplus and of random unicellular maps are built from tilted Brownian trees by identifying points at common heights sampled via local time.
Aldous, The continuum random tree III, Ann
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On breadth-first constructions of scaling limits of random graphs and random unicellular maps
The scaling limits of uniform connected graphs with fixed surplus and of random unicellular maps are built from tilted Brownian trees by identifying points at common heights sampled via local time.