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

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

2004-01-12

arxiv.org/abs/math/0401115v1

Probability Theory and Related Fields 133 (2005) 1--17

Mathematics

Probability

16 pages

Scientific paper

10.1007/s00440-004-0407-2

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 2003) from a bridge with exchangeable increments. Our setting generalizes previous results by allowing a finite number of ``attracting points'' to emerge.

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