19 citations · 27 across the 13 of their papers we have counts for
15 papers
Fluctuations for fully pushed stochastic fronts
Alison Etheridge, Raphaël Forien, Thomas Hughes +1
We study the asymptotic behaviour, in the small noise limit, of stochastic travelling wave solutions to reaction-diffusion equations perturbed by Wright-Fisher noise. Such equation…
Convergence and front position for an FKPP-type free boundary problem
Julien Berestycki, Sarah Penington, Oliver Tough
The free boundary problem\[ \begin{cases} \partial_tu=\frac{1}{2}Δu+u,\quad &t>0, \, x>L_t,\\ u(t,x)=0,\quad &t>0,\, x\le L_t,\\ \int_{L_t}^{\infty}u(t,y)dy=1,\quad &t> 0,\\ u(t,x)…
Branching random walk with non-local competition
Pascal Maillard, Sarah Penington
We study the Bolker-Pacala-Dieckmann-Law (BPDL) model of population dynamics in the regime of large population density. The BPDL model is a particle system in which particles repro…
A branching process with deletions and mergers that matches the threshold for hypercube percolation
Laura Eslava, Sarah Penington, Fiona Skerman
We define a graph process based on a discrete branching process with deletions and mergers, which is inspired by the 4-cycle structure of both the hypercube $Q_d…
Genealogy and spatial distribution of the -particle branching random walk with polynomial tails
Sarah Penington, Matthew I. Roberts, Zsófia Talyigás
The -particle branching random walk is a discrete time branching particle system with selection. We have particles located on the real line at all times. At every time step…
Genealogies in bistable waves
Alison Etheridge, Sarah Penington
We study a model of selection acting on a diploid population (one in which each individual carries two copies of each gene) living in one spatial dimension. We suppose a particular…
Brownian bees in the infinite swarm limit
Julien Berestycki, Eric Brunet, James Nolen +1
The Brownian bees model is a branching particle system with spatial selection. It is a system of particles which move as independent Brownian motions in and inde…
A free boundary problem arising from branching Brownian motion with selection
Julien Berestycki, Éric Brunet, James Nolen +1
We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem a…
Global existence for a free boundary problem of Fisher-KPP type
Julien Berestycki, Eric Brunet, Sarah Penington
Motivated by the study of branching particle systems with selection, we establish global existence for the solution of the free boundary problem \[ \begin{cases} \partial_t…
Branching Brownian motion with decay of mass and the non-local Fisher-KPP equation
Louigi Addario-Berry, Julien Berestycki, Sarah Penington
In this work we study a non-local version of the Fisher-KPP equation, \begin{equation*} \begin{cases} \frac{\partial u}{\partial t}=\tfrac{1}{2}Δu +u (1- ϕ\ast u), \quad t>0, \quad…
The spreading speed of solutions of the non-local Fisher-KPP equation
Sarah Penington
We consider the Fisher-KPP equation with a non-local interaction term. Hamel and Ryzhik showed that in solutions of this equation, the front location at a large time is $\sqrt…
Branching Brownian Motion, mean curvature flow and the motion of hybrid zones
Alison Etheridge, Nic Freeman, Sarah Penington
We provide a probabilistic proof of a well known connection between a special case of the Allen-Cahn equation and mean curvature flow. We then prove a corresponding result for scal…
A central limit theorem for the spatial Lambda Fleming-Viot process with selection
Raphaël Forien, Sarah Penington
We study the evolution of gene frequencies in a population living in , modelled by the spatial Lambda Fleming-Viot process with natural selection (Barton, Etheridge a…
Branching Brownian motion and Selection in the Spatial Lambda-Fleming-Viot Process
Alison Etheridge, Nic Freeman, Sarah Penington +1
We ask the question "when will natural selection on a gene in a spatially structured population cause a detectable trace in the patterns of genetic variation observed in the contem…
The front location in BBM with decay of mass
Louigi Addario-Berry, Sarah Penington
We augment standard branching Brownian motion by adding a competitive interaction between nearby particles. Informally, when particles are in competition, the local resources are i…