23 citations · 40 across the 18 of their papers we have counts for
28 papers
Localisation of the monkey walk with an "impurity" at the origin
Wilfred Armfield, Cécile Mailler
The monkey walk is a model of reinforced random walk introduced by Boyer and Solis-Salas as a model for the exploratory behaviour of capuchin monkeys. At each step of the walk, the…
The forward-loop-erased ants walk
Wilfred Armfield, Cécile Mailler
In this paper, we study a new variant of the ants walk: a model of reinforced random walks for the phenomenon of a colony of ants being able to find the shortest path between their…
A two-table theorem for a disordered Chinese restaurant process
Jakob E. Björnberg, Cécile Mailler, Peter Mörters +1
We investigate a disordered variant of Pitman's Chinese restaurant process where tables carry i.i.d. weights. Incoming customers choose to sit at an occupied table with a probabili…
Scaling limit of critical random trees in random environment
Guillaume Conchon--Kerjan, Daniel Kious, Cécile Mailler
We consider Bienaymé-Galton-Watson trees in random environment, where each generation is attributed a random offspring distribution , and is a sequence o…
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…
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…
Dynamical Models for Random Simplicial Complexes
Nikolaos Fountoulakis, Tejas Iyer, Cécile Mailler +1
We study a general model of random dynamical simplicial complexes and derive a formula for the asymptotic degree distribution. This asymptotic formula encompasses results for a num…
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…
Characterising random partitions by random colouring
Jakob E. Björnberg, Cécile Mailler, Peter Mörters +1
Let be a random partition of the unit interval , i.e. and , and let be i.i.d. Bernoulli r…
Unbiased on-lattice domain growth
Cameron A. Smith, Cécile Mailler, Christian A. Yates
Domain growth is a key process in many areas of biology, including embryonic development, the growth of tissue, and limb regeneration. As a result, mechanisms for incorporating it…
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 -dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to…
Stochastic approximation on non-compact measure spaces and application to measure-valued Pólya processes
Cécile Mailler, Denis Villemonais
Our main result is to prove almost-sure convergence of a stochastic-approximation algorithm defined on the space of measures on a non-compact space. Our motivation is to apply this…
Multiple drawing multi-colour urns by stochastic approximation
Nabil Lasmar, Cécile Mailler, Olfa Selmi
A classical Pólya urn scheme is a Markov process whose evolution is encoded by a replacement matrix . At every discrete time-step, we draw a ball unifo…
A bijective study of Basketball walks
Jérémie Bettinelli, Éric Fusy, Cécile Mailler +1
The Catalan numbers count many classes of combinatorial objects. The most emblematic such objects are probably the Dyck walks and the binary trees, and, whenever another class of c…
Measure-valued Pólya processes
Cécile Mailler, Jean-François Marckert
A Pólya urn process is a Markov chain that models the evolution of an urn containing some coloured balls, the set of possible colours being for .…
Non-extensive condensation in reinforced branching processes
Steffen Dereich, Cecile Mailler, Peter Morters
We study a class of branching processes in which a population consists of immortal individuals equipped with a fitness value. Individuals produce offspring with a rate given by the…
And/or trees: A local limit point of view
Nicolas Broutin, Cécile Mailler
We present here a new and universal approach for the study of random and/or trees, unifying in one framework many different models, including some novel ones not yet understood in…
Condensation and symmetry-breaking in the zero-range process with weak site disorder
Cécile Mailler, Peter Mörters, Daniel Ueltschi
Condensation phenomena in particle systems typically occur as one of two distinct types: either as a spontaneous symmetry breaking in a homogeneous system, in which particle intera…
Generalised and Quotient Models for Random And/Or Trees and Application to Satisfiability
Antoine Genitrini, Cécile Mailler
This article is motivated by the following satisfiability question: pick uniformly at random an and/or Boolean expression of length n, built on a set of k_n Boolean variables. What…
Describing the asymptotic behaviour of multicolour Pólya urns via smoothing systems analysis
Cécile Mailler
The present paper aims at describing in details the asymptotic composition of a class of d-colour Pólya urn: namely balanced, tenable and irreducible urns. We decompose the composi…