3 citations · 4 across the 12 of their papers we have counts for
16 papers
Notes on Kozma and Nitzan's proof of
Arthur Blanc-Renaudie
We present a human intelligible proof of the conjectures of Kozma and Nitzan, that they used to show . The proof was recently found by AI, but was very poorly written. Ou…
Markovian renormalisation for percolation in high-dimension: Semi-decidability of mean field behavior
Arthur Blanc-Renaudie
We develop a new approach to study Bernoulli percolation in dimensions . The key idea is to approximate open paths at probability by a Markov chain of pointed -open…
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^…
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…
The scaling limit of critical hypercube percolation
Arthur Blanc-Renaudie, Nicolas Broutin, Asaf Nachmias
We study the connected components in critical percolation on the Hamming hypercube . We show that their sizes rescaled by converge in distribution, and that,…
Uniform attachment with freezing
Étienne 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…
Uniform attachment with freezing: Scaling limits
Étienne Bellin, Arthur Blanc-Renaudie, Emmanuel Kammerer +1
We investigate scaling limits of trees built by uniform attachment with freezing, which is a variant of the classical model of random recursive trees introduced in a companion pape…
Diameter and long paths in critical digraph
Arthur Blanc-Renaudie
We study the random directed graph in which each of the possible directed edges are present with probability . We show that in the critical window the lon…
A.S. convergence for infinite colour Pólya urns associated with stable random walks
Arthur Blanc-Renaudie
We answer Problem 11.1 of Janson arXiv:1803.04207 on Pólya urns associated with stable random walk. Our proof use neither martingales nor trees, but an approximation with a differe…
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…
Limit of connected multigraph with fixed degree sequence
Arthur Blanc-Renaudie
Motivated by the scaling limits of the connected components of the configuration model, we study uniform connected multigraphs with fixed degree sequence and with sur…
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…
The Foata-Fuchs proof of Cayley's formula, and its probabilistic uses
Louigi Addario-Berry, Serte Donderwinkel, Mickaël Maazoun +1
We present a very simple bijective proof of Cayley's formula due to Foata and Fuchs (1970). This bijection turns out to be very useful when seen through a probabilistic lens; we ex…
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…