• Corpus ID: 15617254

SPDE approximation for random trees

@article{Bakhtin2009SPDEAF,
  title={SPDE approximation for random trees},
  author={Yuri Bakhtin},
  journal={Markov Processes and Related Fields},
  year={2009},
  volume={17},
  pages={1-36}
}
  • Yuri Bakhtin
  • Published 14 September 2009
  • Mathematics
  • Markov Processes and Related Fields
We consider the genealogy tree for a critical branching process conditioned on non-extinction. We enumerate vertices in each generation of the tree so that for each two generations one can define a monotone map describing the ancestor--descendant relation between their vertices. We show that under appropriate rescaling this family of monotone maps converges in distribution in a special topology to a limiting flow of discontinuous monotone maps which can be seen as a continuum tree. This flow is… 
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