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math.PR2026
Subcritical annulus crossing in spatial random graphs
Emmanuel Jacob, Benedikt Jahnel, Lukas Lüchtrath
We consider general continuum percolation models obeying sparseness, translation invariance, and spatial decorrelation. In particular, this includes models constructed on general p…
math.PR2025
The snake in the Brownian sphere
Omer Angel, Emmanuel Jacob, Brett Kolesnik +1
The Brownian sphere is a random metric space, homeomorphic to the two-dimensional sphere, which arises as the universal scaling limit of many types of random planar maps. The direc…
math.PR2024
Only long edges can erase the subcritical annulus-crossing phase of weight-dependent random connection models
Emmanuel Jacob
This short note aims at complementing the results of the recent work arXiv:2302.05396, where Jahnel and Lüchtrath investigate the question of existence of a subcritical percolatio…