23 citations · 40 across the 18 of their papers we have counts for
5 papers · 2 filters
Fluctuations of balanced urns with infinitely many colours
Svante Janson, Cécile Mailler, Denis Villemonais
In this paper, we prove convergence and fluctuation results for measure-valued Pólya processes (MVPPs, also known as Pólya urns with infinitely-many colours). Our convergence resul…
Parametrised branching processes: a functional version of Kesten \& Stigum theorem
Cécile Mailler, Jean-François Marckert
Let be a supercritical Galton-Watson process whose offspring distribution has mean and is such that . According to the fa…
The trace-reinforced ants process does not find shortest paths
Daniel Kious, Cécile Mailler, Bruno Schapira
In this paper, we study a probabilistic reinforcement-learning model for ants searching for the shortest path(s) between their nest and a source of food. In this model, the nest an…
Large deviations principle for a stochastic process with random reinforced relocations
Erion-Stelios Boci, Cécile Mailler
Stochastic processes with random reinforced relocations have been introduced in the physics literature to model animal foraging behaviour. Such a process evolves as a Markov proces…
Voronoi cells in random split trees
Alexander Drewitz, Markus Heydenreich, Cécile Mailler
We study the sizes of the Voronoi cells of uniformly chosen vertices in a random split tree of size . We prove that, for large, the largest of these Voronoi cells co…