6 papers
Super-Brownian limits and the -point function for high-dimensional percolation
Arthur Blanc-Renaudie, Tom Hutchcroft
We prove that there exist positive constants and such that the high-dimensional critical percolation -point function is given by \[ T_{p_c}(x_1,x_2,\ldots,x_{k}) \sim V^…
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…
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…
Limit of trees with fixed degree sequence
Arthur Blanc-Renaudie
We show, under natural conditions, that uniform rooted trees with fixed degree sequence converge after renormalization toward inhomogeneous continuum random trees (ICRT). We also p…
Uniform attachment with freezing
Ãtienne Bellin, Arthur Blanc-Renaudie, Emmanuel Kammerer +1
In the classical model of random recursive trees, trees are recursively built by attaching new vertices to old ones. What happens if vertices are allowed to freeze, in the sense th…
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 …