Cécile Mailler

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20182021

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7 papers · 1 filter

math.PR2021

Parametrised branching processes: a functional version of Kesten \& Stigum theorem

Cécile Mailler, Jean-François Marckert

Let $(Z_{n}, n \geq 0)$ be a supercritical Galton-Watson process whose offspring distribution $μ$ has mean $λ > 1$ and is such that $\int x (lo g (x))_{+} d μ (x) < + \infty$ . According to the fa…

math.PR2021

Voronoi cells in random split trees

Alexander Drewitz, Markus Heydenreich, Cécile Mailler

We study the sizes of the Voronoi cells of $k$ uniformly chosen vertices in a random split tree of size $n$ . We prove that, for $n$ large, the largest of these $k$ Voronoi cells co…

math.PR2020

Finding geodesics on graphs using reinforcement learning

Daniel Kious, Cécile Mailler, Bruno Schapira

It is well-known in biology that ants are able to find shortest paths between their nest and the food by successive random explorations, without any mean of communication other tha…

math.PR2019

Competing growth processes with random growth rates and random birth times

Cécile Mailler, Peter Mörters, Anna Senkevich

Finding the most powerful node in a dynamic random network, the largest set in a partition-valued stochastic process, or the largest family in an evolving population at a given tim…

math.PR2019

Characterising random partitions by random colouring

Jakob E. Björnberg, Cécile Mailler, Peter Mörters +1

Let $(X_{1}, X_{2}, ...)$ be a random partition of the unit interval $[0, 1]$ , i.e. $X_{i} \geq 0$ and $\sum_{i \geq 1} X_{i} = 1$ , and let $(ε_{1}, ε_{2}, ...)$ be i.i.d. Bernoulli r…

math.PR2018

Random walks with preferential relocations and fading memory: a study through random recursive trees

Cécile Mailler, Gerónimo Uribe Bravo

Consider a stochastic process that behaves as a $d$ -dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to…