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Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees

  • Author(s): Aldous, D
  • Miermont, G
  • Pitman, J
  • et al.
Abstract

We study the asymptotics of the p-mapping model of random mappings on [n] as n gets large, under a large class of asymptotic regimes for the underlying distribution p. We encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees, this exploration process being derived (Aldous-Miermont-Pitman 2004) from a bridge with exchangeable increments. Our setting generalizes previous results by allowing a finite number of "attracting points" to emerge. © Springer-Verlag 2005.

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