49 citations · 272 across the 48 of their papers we have counts for
54 papers
Elephants explore in spirals sometimes
Lucile Laulin, Bastien Mallein
We consider in this article an Elephant Random Walk evolving in the plane. Specifically, this is a reinforced stochastic process in which the th step is given by a random rotati…
Selection of the fittest or selection of the luckiest: the emergence of Goodhart's law in evolution
Bastien Mallein, Francesco Paparella, Emmanuel Schertzer +1
Biological evolution depends on the passing down to subsequent generations of genetic information encoding beneficial traits, and on the removal of unfit individuals by a selection…
Reinforced Galton--Watson processes III: Empirical offspring distributions
Jean Bertoin, Bastien Mallein
Reinforced Galton--Watson processes describe the dynamics of a population where reproduction events are reinforced, in the sense that offspring numbers of forebears can be repeated…
The Derrida-Retaux model on a geometric Galton-Watson tree
Gerold Alsmeyer, Yueyun Hu, Bastien Mallein
We consider a generalized Derrida-Retaux model on a Galton-Watson tree with a geometric offspring distribution. For a class of recursive systems, including the Derrida-Retaux model…
The longest branches in a non-Markovian phylogenetic tree
Sergey Bocharov, Simon C. Harris, Bastien Mallein
Consider a Bellman--Harris-type branching process, in which individuals evolve independently of one another, giving birth after a random time to a random number of children…
The Yaglom limit for branching Brownian motion with absorption and slightly subcritical drift
Julien Berestycki, Jiaqi Liu, Bastien Mallein +1
Consider branching Brownian motion with absorption in which particles move independently as one-dimensional Brownian motions with drift , each particle splits into two particle…
Phase transition of the consistent maximal displacement of branching Brownian motion
Julien Berestycki, Jiaqi Liu, Bastien Mallein +1
Consider branching Brownian motion in which we begin with one particle at the origin, particles independently move according to Brownian motion, and particles split into two at rat…
Extremal Process of Last Progeny Modified Branching Random Walks
Partha Pratim Ghosh, Bastien Mallein
We consider a last progeny modified branching random walk, in which the position of each particle at the last generation is modified by an i.i.d. copy of a random variable .…
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…
Fragmentation processes and the convex hull of the Brownian motion in a disk
Bénédicte Haas, Bastien Mallein
Motivated by the study of the convex hull of the trajectory of a Brownian motion in the unit disk reflected orthogonally at its boundary, we study inhomogeneous fragmentation proce…
Last passage percolation and limit theorems in Barak-Erdős directed random graphs and related models
Sergey Foss, Takis Konstantopoulos, Bastien Mallein +1
We consider directed random graphs, the prototype of which being the Barak-Erdős graph , and study the way that long (or heavy, if weights are present) paths…
Reinforced Galton-Watson processes II: Large time behaviors
Jean Bertoin, Bastien Mallein
Reinforced Galton-Watson processes have been introduced in arxiv:2306.02476 as population models with non-overlapping generations, such that reproduction events along genealogical…
Reinforced Galton-Watson processes I: Malthusian exponents
Jean Bertoin, Bastien Mallein
In a reinforced Galton-Watson process with reproduction law and memory parameter , the number of children of a typical individual either, with probability…
KPP traveling waves in the half-space
Julien Berestycki, Cole Graham, Yujin H. Kim +1
We study traveling waves of the KPP equation in the half-space with Dirichlet boundary conditions. We show that minimal-speed waves are unique up to translation and rotation but fa…
On the length of the shortest path in a sparse Barak-Erdős graph
Bastien Mallein, Pavel Tesemnikov
We consider an inhomogeneous version of the Barak-Erdős graph, i.e. a directed Erős-Rényi random graph on with no loop. Given a Riemann-integrable non-negative…
The extremal point process of branching Brownian motion in
Julien Berestycki, Yujin H. Kim, Eyal Lubetzky +2
We consider a branching Brownian motion in with in which the position of a particle at time can be encoded by its dire…
Estimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation
Sergey Foss, Takis Konstantopoulos, Bastien Mallein +1
Our object of study is the asymptotic growth of heaviest paths in a charged (weighted with signed weights) complete directed acyclic graph. Edge charges are i.i.d. random variables…
Late levels of nested occupancy scheme in random environment
Alexander Iksanov, Bastien Mallein
Consider a weighted branching process generated by a point process on , whose atoms sum up to one. Then the weights of all individuals in any given generation sum up to one,…
On the branching convolution equation
Pascal Maillard, Bastien Mallein
We characterize all random point measures which are in a certain sense stable under the action of branching. Denoting by the branching convolution operation introduce…
A necessary and sufficient condition for the convergence of the derivative martingale in a branching Lévy process
Bastien Mallein, Quan Shi
A continuous-time particle system on the real line satisfying the branching property and an exponential integrability condition is called a branching Lévy process, and its law is c…
Total number of births on the negative half-line of the binary branching Brownian motion in the boundary case
Xinxin Chen, Bastien Mallein
The binary branching Brownian motion in the boundary case is a particle system on the real line behaving as follows. It starts with a unique particle positioned at the origin at ti…
A tractable non-adaptative group testing method for non-binary measurements
Emilien Joly, Bastien Mallein
The original problem of group testing consists in the identification of defective items in a collection, by applying tests on groups of items that detect the presence of at least o…
Anomalous spreading in reducible multitype branching Brownian motion
Mohamed Ali Belloum, Bastien Mallein
We consider a two-type reducible branching Brownian motion, defined as a particle system on the real line in which particles of two types move according to independent Brownian mot…
Branching Brownian motion conditioned on small maximum
Xinxin Chen, Hui He, Bastien Mallein
We consider a standard binary branching Brownian motion on the real line. It is known that the maximal position among all particles alive at time , shifted by $m_t = \sqrt…