%0 Generic %1 arXiv:math.PR/0401115 %A Aldous, David J. %A Miermont, Gregory %A Pitman, Jim %D 2004 %K author_pitman_from_arxiv %T Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees. %U http://arxiv.org/abs/math.PR/0401115 %X 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.

@misc{arXiv:math.PR/0401115, 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 2003) from a bridge with exchangeable increments. Our setting generalizes previous results by allowing a finite number of ``attracting points'' to emerge.}, added-at = {2008-01-25T05:29:59.000+0100}, arxiv = {arXiv:math.PR/0401115}, author = {Aldous, David J. and Miermont, Gregory and Pitman, Jim}, biburl = {https://www.bibsonomy.org/bibtex/2284b09be03d0481eedad72fea9dd7305/pitman}, interhash = {92d082b390633ad93a2818c0e3e807cf}, intrahash = {284b09be03d0481eedad72fea9dd7305}, keywords = {author_pitman_from_arxiv}, timestamp = {2008-01-25T05:33:08.000+0100}, title = {{Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees.}}, url = {http://arxiv.org/abs/math.PR/0401115}, year = 2004 }