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Let T t be a critical binary continuous-time Galton-Watson tree size-biased according to the number of particles at time t. Decompose the population at t according to the particles' degree of relationship with a distinguished particle picked purely at random from those alive at t. Keeping track of the times when the different families grow out of the… (More)

The genealogy of a cluster in the multitype voter model can be defined in terms of a family of dual coalescing random walks. We represent the genealogy of a cluster as a point process in a size-time plane and show that in high dimensions the genealogy of the cluster at the origin has a weak Poisson limit. The limiting point process is the same as for the… (More)

- Jochen Geiger
- 2010

Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent. Regard a discrete probability distribution as a fragmentation of unit mass into different clusters, where the weights of the distribution correspond to cluster masses. The additive coalescent is the Markov process on the set of ranked discrete probability… (More)

- Jochen Geiger
- 2007

- Jochen Geiger
- 2006

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