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.
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Research supported by NSF Grant DMS-0203062.
Research supported by NSF Grant DMS-0071468.
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Aldous, D., Miermont, G. & Pitman, J. Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees. Probab. Theory Relat. Fields 133, 1–17 (2005). https://doi.org/10.1007/s00440-004-0407-2
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DOI: https://doi.org/10.1007/s00440-004-0407-2