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
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随机p映射的弱收敛性和非齐次连续随机树的探索过程
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
J. Pitman
中科院分区：
文献类型：
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作者：
D. Aldous;G. Miermont;J. Pitman
我们研究了[n]上随机映射的p映射模型的渐近性，当n变大时，在潜在分布p的一大类渐近区域下。我们将这些随机映射编码为随机游走，这些随机游走被证明收敛于非齐次随机树的探索过程的函数，这个探索过程是由一个具有可交换增量的桥推导出来的（Aldous-Miermont-Pitman 2004）。我们的设置通过允许出现有限数量的“吸引点”来推广先前的结果。
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.