5 papers
Critical percolation on the discrete torus in high dimensions
Arthur Blanc-Renaudie, Asaf Nachmias
We consider percolation on the discrete torus at , the critical value for percolation on the corresponding infinite lattice , and…
A phase transition for the biased tree-builder random walk
Arthur Blanc-Renaudie, Camille Cazaux, Guillaume Conchon-Kerjan +2
We consider a recent model of random walk that recursively grows the network on which it evolves, namely the Tree Builder Random Walk (TBRW). We introduce a bias …
Scaling limit of trees with vertices of fixed degrees and heights
Arthur Blanc-Renaudie, Emmanuel Kammerer
We consider large uniform random trees where we fix for each vertex its degree and height. We prove, under natural conditions of convergence for the profile, that those trees prope…
Looptree, Fennec, and Snake of ICRT
Arthur Blanc-Renaudie
We introduce a new theory of plane -tree, to define plane ICRT (inhomogeneous continuum random tree), and its looptree, fennec (a Gaussian free field on the looptree), a…
Compactness and fractal dimensions of inhomogeneous continuum random trees
Arthur Blanc-Renaudie
We introduce a new stick-breaking construction for inhomogeneous continuum random trees (ICRT). This new construction allows us to prove the necessary and sufficient condition for…