A N-branching random walk with random selection

作者:Cortines Aser*; Mallein Bastien
来源:Alea (Rio de Janeiro): Latin American Journal of Probability and Mathematical Statistics , 2017, 14(1): 117-137.
DOI:10.30757/alea.v14-07

摘要

We consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with N individuals on the real line. At each time step, every individual reproduces independently, and its offspring are positioned around its current locations. Among all children, N individuals are sampled at random without replacement to form the next generation, such that an individual at position x is chosen with probability proportional to c(beta x). We compute the asymptotic speed and the genealogical behavior of the system.

  • 出版日期2017

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