Random Weil-Petersson punctured spheres converge, after fourth-root rescaling, to the Brownian sphere.
A random walk among random graphs
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abstract
Lecture notes of a master course given at Orsay between 2019-2024. Topics covered include Part I: One-dimensional random walks, cycle lemma and Bienaym\'e--Galton--Watson random trees. Part II: Erd\"os--R\'enyi random graphs, three proofs of the emergence of the giant component. Part III: Random recursive tree, random permutations and continuous time embedding techniques. Intended for publication.
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Random punctured hyperbolic surfaces & the Brownian sphere
Random Weil-Petersson punctured spheres converge, after fourth-root rescaling, to the Brownian sphere.