Extremal process for irreducible multitype branching Brownian motion

H Hou, YX Ren, R Song - arXiv preprint arXiv:2303.12256, 2023 - arxiv.org
We first study the convergence of solutions of a system of F-KPP equations related to
irreducible multitype branching Brownian motions with Heaviside-type initial conditions to …

Double jump in the maximum of two-type reducible branching Brownian motion

H Ma, YX Ren - arXiv preprint arXiv:2305.09988, 2023 - arxiv.org
Consider a two-type reducible branching Brownian motion in which particles' diffusion
coefficients and branching rates are influenced by their types. Here reducible means that …

The extremal process of a cascading family of branching Brownian motion

MA Belloum - arXiv preprint arXiv:2202.01584, 2022 - arxiv.org
We study the asymptotic behaviour of the extremal process of a cascading family of
branching Brownian motions. This is a particle system on the real line such that each particle …

Asymptotic Expansions for Additive Measures of Branching Brownian Motions

H Hou, YX Ren, R Song - Journal of Theoretical Probability, 2024 - Springer
Let N (t) be the collection of particles alive at time t in a branching Brownian motion
in\(\mathbb {R}^ d\), and for\(u\in N (t)\), let\({\textbf {X}} _u (t)\) be the position of particle u at …

Limiting distributions for a class of super-Brownian motions with spatially dependent branching mechanisms

YX Ren, T Yang - Journal of Theoretical Probability, 2024 - Springer
In this paper, we consider a large class of super-Brownian motions in R with spatially
dependent branching mechanisms. We establish the almost sure growth rate of the mass …

A simple backward construction of branching Brownian motion with large displacement and applications

J Berestycki, É Brunet, A Cortines… - Annales de l'Institut …, 2022 - projecteuclid.org
In this article, we study the extremal processes of branching Brownian motions conditioned
on having an unusually large maximum. The limiting point measures form a one-parameter …

The extremal process of branching Brownian motion with absorption

F Yang, Y Zhu - Electronic Journal of Probability, 2024 - projecteuclid.org
In this paper, we study branching Brownian motion with absorption, in which particles
undergo Brownian motions with drift and are killed upon reaching the origin. We prove that …

From 0 to 3: Intermediate phases between normal and anomalous spreading of two-type branching Brownian motion

H Ma, YX Ren - arXiv preprint arXiv:2312.13595, 2023 - arxiv.org
The logarithmic correction for the order of the maximum of a two-type reducible branching
Brownian motion on the real line exhibits a double jump when the parameters (the ratio of …

Branching Brownian motion with generation-dependent diffusivity and nonlocal partial differential equations

A Dunlap, L Ryzhik - arXiv preprint arXiv:2312.17139, 2023 - arxiv.org
We study a voting model on a branching Brownian motion process on $\mathbb {R} $ in
which the diffusivity of each child particle is increased from that of the parent by a factor of …

On the branching convolution equation

P Maillard, B Mallein - Electronic Communications in Probability, 2021 - projecteuclid.org
We characterize all random point measures which are in a certain sense stable under the
action of branching. Denoting by⊛ the branching convolution operation introduced by …