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The genealogy of an exactly solvable Ornstein-Uhlenbeck type branching process with selection. (English) Zbl 1406.60130
Summary: We study the genealogy of an exactly 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 gives birth to children around \(a\) times its current position, where \(a>0\) is a parameter of the model. Then, the \(N\) rightmost newborn children are selected to form the next generation. We show that the genealogy of the process converges toward a Beta coalescent as \(N \rightarrow \infty \). The process we consider can be seen as a toy model version of a continuous-time branching process with selection, in which particles move according to independent Ornstein–Uhlenbeck processes. The parameter \(a\) is akin to the pulling strength of the Ornstein–Uhlenbeck process.
60K35 Interacting random processes; statistical mechanics type models; percolation theory
92D15 Problems related to evolution
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