The genealogy of branching Brownian motion with absorption

@article{Berestycki2013TheGO,
  title={The genealogy of branching Brownian motion with absorption},
  author={Julien Berestycki and Nathanael Berestycki and Jason Schweinsberg},
  journal={Annals of Probability},
  year={2013},
  volume={41},
  pages={527-618}
}
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 constant with approximately N particles. We show that the characteristic time scale for the evolution of this population is of order (logN) 3 , in the sense that when time is measured in these units, the scaled number of particles converges to a variant of Neveu’s continuous-state branching process… 

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References

SHOWING 1-10 OF 84 REFERENCES

Branching diffusion processes in population genetics

  • S. Sawyer
  • Mathematics
    Advances in Applied Probability
  • 1976
A branching random field is considered as a model of either of two situations in genetics in which migration or dispersion plays a role. Specifically we consider the expected number of individuals NA

Maximal displacement of branching brownian motion

It is shown that the position of any fixed percentile of the maximal displacement of standard branching Brownian motion in one dimension is 21/2t–3 · 2−3/2 log t + O(1) at time t, the second-order

THE COALESCENT

Stochastic flows associated to coalescent processes

Abstract. We study a class of stochastic flows connected to the coalescent processes that have been studied recently by Möhle, Pitman, Sagitov and Schweinsberg in connection with asymptotic models

Survival of Near-Critical Branching Brownian Motion

Consider a system of particles performing branching Brownian motion with negative drift $\mu= \sqrt{2 - \varepsilon}$ and killed upon hitting zero. Initially there is one particle at x>0. Kesten

Coalescents with multiple collisions

k−2 � 1 − xb−k � � dx� . Call this process a � -coalescent. Discrete measure-valued processes derived from the � -coalescent model a system of masses undergoing coalescent collisions. Kingman's

The general coalescent with asynchronous mergers of ancestral lines

  • S. Sagitov
  • Mathematics
    Journal of Applied Probability
  • 1999
Take a sample of individuals in the fixed-size population model with exchangeable family sizes. Follow the ancestral lines for the sampled individuals backwards in time to observe the ancestral

Recent progress in coalescent theory

Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of

The number of absorbed individuals in branching Brownian motion with a barrier

We study supercritical branching Brownian motion on the real line starting at the origin and with constant drift $c$. At the point $x > 0$, we add an absorbing barrier, i.e.\ individuals touching the

Multiplicative Martingales for Spatial Branching Processes

Out of simplicity, we restrict ourselves to consider the dyadic brownian branching process (Nt, t ∈ R+) on the real line. By definition of this process, its particles perform independent brownian
...