1 citations · 1 across the 7 of their papers we have counts for
7 papers
Typical distances in high-genus triangulations
Tanguy Lions
We study the distance between two uniformly chosen points on a uniform random triangulation whose genus g is proportional to the number of faces 2n. We show that the distance resca…
Local limits of uniform triangulations with boundaries in high genus
Tanguy Lions
We study the local limits of uniform random triangulations with boundaries in the regime where the genus is proportional to the number of faces. Budzinski and Louf proved in 2020 t…
Large expander subgraphs in high genus triangulations
Tanguy Lions, Baptiste Louf
We prove that random triangulations of high genus contain very large expander subgraphs, answering a question of Benjamini. Our approach relies on new general criteria for arbitrar…
The tight length spectrum of large-genus random hyperbolic surfaces with many cusps
Timothy Budd, Tanguy Lions
Since the work of Mirzakhani and Petri on random hyperbolic surfaces of large genus, length statistics of closed geodesics have been studied extensively. We focus on the case of ra…
Quenched scaling limit of critical percolation clusters on Galton-Watson trees
Eleanor Archer, Tanguy Lions
We consider quenched critical percolation on a supercritical Galton--Watson tree with either finite variance or -stable offspring tails for some . We show that the G…
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 …
Quenched invariance principle for biased random walks in random conductances in the sub-ballistic regime
Alexander Fribergh, Tanguy Lions, Carlo Scali
We consider a biased random walk in positive random conductances on for . In the sub-ballistic regime, we prove the quenched convergence of the properly res…