23 citations · 38 across the 14 of their papers we have counts for
16 papers
Fractal properties of the frontier in Poissonian coloring
Anne-Laure Basdevant, Guillaume Blanc, Nicolas Curien +1
We study a model of random partitioning by nearest-neighbor coloring from Poisson rain, introduced independently by Aldous and Preater. Given two initial points in respec…
Reversible Poisson-Kirchhoff Systems
Alexandre Boyer, Jérôme Casse, Nathanaël Enriquez +1
We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This in…
Once reinforced random walk on
Daniel Kious, Bruno Schapira, Arvind Singh
We revisit an unpublished paper of Vervoort (2002) on the once reinforced random walk, and prove that this process is recurrent on any graph of the form , with…
The geometry of a critical percolation cluster on the UIPT
Matthias Gorny, Édouard Maurel-Segala, Arvind Singh
We consider a critical Bernoulli site percolation on the uniform infinite planar triangulation. We study the tail distributions of the peeling time, perimeter, and volume of the hu…
From Hammersley's lines to Hammersley's trees
Anne-Laure Basdevant, Lucas Gerin, Jean-Baptiste Gouere +1
We construct a stationary random tree, embedded in the upper half plane, with prescribed offspring distribution and whose vertices are the atoms of a unit Poisson point process. Th…
Percolation by cumulative merging and phase transition for the contact process on random graphs
Laurent Ménard, Arvind Singh
Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both cl…