• Corpus ID: 240354684

# A branching particle system as a model of semi pushed fronts

@inproceedings{Tourniaire2021ABP,
title={A branching particle system as a model of semi pushed fronts},
author={Julie Tourniaire},
year={2021}
}
We consider a system of particles performing a one-dimensional dyadic branching Brownian motion with space-dependent branching rate, negative drift −μ and killed upon reaching 0, starting with N particles. More precisely, particles branch at rate ρ/2 in the interval [0, 1], for some ρ > 1, and at rate 1/2 in (1,+∞). The drift μ(ρ) is chosen in such a way that, heuristically, the system is critical in some sense: the number of particles stays roughly constant before it eventually dies out. This…
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## References

SHOWING 1-10 OF 46 REFERENCES

### Speed and fluctuations of N-particle branching Brownian motion with spatial selection

We consider branching Brownian motion on the real line with the following selection mechanism: every time the number of particles exceeds a (large) given number N, only the N right-most particles are

### Particle configurations for branching Brownian motion with an inhomogeneous branching rate

• Mathematics
• 2021
Aiming to understand the distribution of fitness levels of individuals in a large population undergoing selection, we study the particle configurations of branching Brownian motion where each

### The genealogy of branching Brownian motion with absorption

• Mathematics
• 2013
We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the near-critical regime where the total population stays roughly

### Yaglom-type limit theorems for branching Brownian motion with absorption

• Mathematics
Annales Henri Lebesgue
• 2022
We consider one-dimensional branching Brownian motion in which particles are absorbed at the origin. We assume that when a particle branches, the offspring distribution is supercritical, but the

### Brunet-Derrida Behavior of Branching-Selection Particle Systems on the Line

• Mathematics
• 2008
We consider a class of branching-selection particle systems on $${\mathbb{R}}$$ similar to the one considered by E. Brunet and B. Derrida in their 1997 paper “Shift in the velocity of a front due to

### An invariance principle for branching diffusions in bounded domains

We study branching diffusions in a bounded domain D of $$\mathbb {R}^d$$Rd in which particles are killed upon hitting the boundary $$\partial D$$∂D. It is known that any such process undergoes a

### Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization.

• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2007
A family of models describing the evolution under selection of a population whose dynamics can be related to the propagation of noisy traveling waves, and one striking result is that, for this particular model, the genealogical trees have the same statistics as the trees of replicas in the Parisi mean-field theory of spin glasses.

### Local extinction versus local exponential growth for spatial branching processes

• Mathematics
• 2004
Let X be either the branching diffusion corresponding to the operator Lu+β(u2−u) on D⊆ Rd [where β(x)≥0 and β≡0 is bounded from above] or the superprocess corresponding to the operator Lu+βu−αu2 on

### The genealogy of an exactly solvable Ornstein–Uhlenbeck type branching process with selection

• Mathematics
• 2018
We study the genealogy of a solvable population model with N particles on the real line which evolves according to a discrete-time branching process with selection. At each time step, every particle