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7 papers · 2 filters
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 …
Ideal Poisson--Voronoi tessellations beyond hyperbolic spaces
Matteo D'Achille
We construct and study the ideal Poisson--Voronoi tessellation of the product of two hyperbolic planes endowed with the norm. We prove…
Genetic contribution of an advantaged mutant in the biparental Moran model -- finite selection
Camille Coron, Yves Le Jan
We consider a population of N individuals, whose dynamics through time is represented by a biparental Moran model with two types: an advantaged type and a disadvantaged type. The a…
Local limit of massive spanning forests on the complete graph
Matteo D'Achille, Nathanaël Enriquez, Paul Melotti
We identify the local limit of massive spanning forests on the complete graph. This generalizes a well-known theorem of Grimmett on the local limit of uniform spanning trees on the…
The height gap of planar Brownian motion is
Antoine Jego, Titus Lupu, Wei Qian
We show that the occupation measure of planar Brownian motion exhibits a constant height gap of across its outer boundary. This property bears similarities with the celebrate…
Freezing in the Infinite-Bin Model
Bastien Mallein, Sanjay Ramassamy, Arvind Singh
The infinite-bin model is a one-dimensional particle system on introduced by Foss and Konstantopoulos in relation with last passage percolation on complete directed ac…