4 papers
A phase transition in ErdÅs-Barak random graphs
Gilles Blanchard, Nicolas Curien, Klara Krause +1
We study monotone paths in ErdÅs-Rényi random graphs on numbered vertices. Benjamini & Tzalik established a phase transition at for this model. We refine t…
Where do (random) trees grow leaves?
Alessandra Caraceni, Nicolas Curien, Robin Stephenson
We study a model of random binary trees grown "by the leaves" in the style of Luczak and Winkler. If is a uniform plane binary tree of size , Luczak and Winkler, and late…
Recurrence of the plane Elephant random walk
Nicolas Curien, Lucile Laulin
We give a short proof of the recurrence of the two-dimensional elephant random walk in the diffusive regime. This was recently established by Shuo Qin, but our proof only uses very…
A random walk among random graphs
Nicolas Curien
Lecture notes of a master course given at Orsay between 2019-2024. Topics covered include Part I: One-dimensional random walks, cycle lemma and Bienaymé--Galton--Watson random tre…