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Article Dans Une Revue Probability Theory and Related Fields Année : 2005

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

Résumé

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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Dates et versions

hal-00001018 , version 1 (12-01-2004)

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David Aldous, Grégory Miermont, Jim Pitman. Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees. Probability Theory and Related Fields, 2005, 133, pp.1--17. ⟨10.1007/s00440-004-0407-2⟩. ⟨hal-00001018⟩
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