Bastien Mallein
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Bastien Mallein has a total of 8 co-authors. Here are the top co-authors by number of shared publications:
- Julien Berestycki
Department of Statistics and Magdalen College, University of Oxford, Oxford, UK
2 shared publications - Arvind Singh
CNRS and LMO, Université Paris-Saclay
1 shared publication - Cole Graham
University of Wisconsin–Madison, Madison, USA
1 shared publication - Jason Schweinsberg
Department of Mathematics University of California San Diego
1 shared publication - Jean Bertoin
Institute of Mathematics, University of Zurich, Zurich, Switzerland
1 shared publication - Jiaqi Liu
University of Pennsylvania
1 shared publication
Latest Publications
- Open Access
- 21 October 2025
- Published by Springer Nature in Probability Theory and Related Fields
- Vol. 196 (3-4) , 1-34
Reinforced Galton–Watson processes III: Empirical offspring distributions
Reinforced Galton–Watson processes describe the dynamics of a population where reproduction events are reinforced, in the sense that offspring numbers of forbearers can be repeated randomly by descendants. More specifically, the evolution depends on the empirical offspring distribution of each individual along its ancestral lineage. We are interested here in asymptotic properties of the empirical distributions observed in the population, such as concentration, evanescence and persistence. For this, we incorporate tools from the theory of large deviations to our preceding analysis [4, 5].
- 21 October 2025
- Published by Springer Nature in Probability Theory and Related Fields
- Vol. 196 (3-4) , 1-34
Open AccessReinforced Galton–Watson processes III: Empirical offspring distributions
Reinforced Galton–Watson processes describe the dynamics of a population where reproduction events are reinforced, in the sense that offspring numbers of forbearers can be repeated randomly by descendants. More specifically, the evolution depends on the empirical offspring distribution of each individual along its ancestral lineage. We are interested here in asymptotic properties of the empirical distributions observed in the population, such as concentration, evanescence and persistence. For this, we incorporate tools from the theory of large deviations to our preceding analysis [4, 5].
- 3 October 2025
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 406 (11) , 1-53
KPP Traveling Waves in the Half-Space
- 3 October 2025
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 406 (11) , 1-53
KPP Traveling Waves in the Half-Space
- Open Access
The Yaglom limit for branching Brownian motion with absorption and slightly subcritical drift
Consider branching Brownian motion with absorption in which particles move independently as one-dimensional Brownian motions with drift $-ρ$, each particle splits into two particles at rate one, and particles are killed when they reach the origin. Kesten (1978) showed that this process dies out with probability one if and only if $ρ\geq \sqrt{2}$. We show that in the subcritical case when $ρ> \sqrt{2}$, the law of the process conditioned on survival until time $t$ converges as $t \rightarrow \infty$ to a quasi-stationary distribution, which we call the Yaglom limit. We give a construction of this quasi-stationary distribution. We also study the asymptotic behavior as $ρ\downarrow \sqrt{2}$ of this quasi-stationary distribution. We show that the logarithm of the number of particles and the location of the highest particle are of order $ε^{-1/3}$, and we obtain a limit result for the empirical distribution of the particle locations.Open AccessThe Yaglom limit for branching Brownian motion with absorption and slightly subcritical drift
Consider branching Brownian motion with absorption in which particles move independently as one-dimensional Brownian motions with drift $-ρ$, each particle splits into two particles at rate one, and particles are killed when they reach the origin. Kesten (1978) showed that this process dies out with probability one if and only if $ρ\geq \sqrt{2}$. We show that in the subcritical case when $ρ> \sqrt{2}$, the law of the process conditioned on survival until time $t$ converges as $t \rightarrow \infty$ to a quasi-stationary distribution, which we call the Yaglom limit. We give a construction of this quasi-stationary distribution. We also study the asymptotic behavior as $ρ\downarrow \sqrt{2}$ of this quasi-stationary distribution. We show that the logarithm of the number of particles and the location of the highest particle are of order $ε^{-1/3}$, and we obtain a limit result for the empirical distribution of the particle locations. - Open Access
Freezing in the Infinite-Bin Model
The infinite-bin model is a one-dimensional particle system on Z introduced by Foss and Konstantopoulos in relation with last passage percolation on complete directed acyclic graphs. In this model, at each integer time, a particle is selected at random according to its rank, and produces a child at the location immediately to its right. In this article, we consider the limiting distribution of particles after an infinite number of branching events have occurred. Under mild assumptions, we prove that the event (called freezing) that a location contains only a finite number of balls satisfies a 0-1 law and we provide various criteria to determine whether freezing occurs.
Open AccessFreezing in the Infinite-Bin Model
The infinite-bin model is a one-dimensional particle system on Z introduced by Foss and Konstantopoulos in relation with last passage percolation on complete directed acyclic graphs. In this model, at each integer time, a particle is selected at random according to its rank, and produces a child at the location immediately to its right. In this article, we consider the limiting distribution of particles after an infinite number of branching events have occurred. Under mild assumptions, we prove that the event (called freezing) that a location contains only a finite number of balls satisfies a 0-1 law and we provide various criteria to determine whether freezing occurs.