7 papers
Rémy's diffusion on Brownian trees
Nicolas Curien, Cyril Marzouk
Rémy's algorithm is a famous recursive construction of uniform random binary trees of growing size by a local grafting operation. In this work we construct a continuous version, a…
Critical Self-Similar Markov Trees
Nicolas Curien, Xingjian Hu, Dongjian Qian
Recently introduced and studied in arXiv:2407.07888, a self-similar Markov tree (ssMt) is a random decorated tree that vastly generalises the fragmentation tree. We study here the…
Growing Self-Similar Markov Trees
Nicolas Curien, William Fleurat, Adrianus Twigt
Can we obtain a Brownian CRT of mass from a CRT of mass by cutting certain branches? In this paper, we will answer that question in the much more general setting of self-…
Random punctured hyperbolic surfaces & the Brownian sphere
Timothy Budd, Nicolas Curien
We consider random genus-0 hyperbolic surfaces with punctures, sampled according to the Weil-Petersson measure. We show that, after rescaling the metric by…
The scaling limit of planar maps with large faces
Nicolas Curien, Grégory Miermont, Armand Riera
We prove that large Boltzmann stable planar maps of index converge in the scaling limit towards a random compact metric space that we construct expli…
Self-similar Markov trees and scaling limits
Jean Bertoin, Nicolas Curien, Armand Riera
Self-similar Markov trees constitute a remarkable family of random compact real trees carrying a decoration function that is positive on the skeleton. As the terminology suggests,…