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• W4240348261 abstract "Abstract Let X n be the number of cuts needed to isolate the root in a random recursive tree with n vertices. We provide a weak convergence result for X n . The basic observation for its proof is that the probability distributions of ${X_n: n=2,3,ldots}$ are recursively defined by $X_n {{rm d}atop{=}} X_{n-D_n} + 1, ; n=2,3,ldots, ; X_1=0$ , where D n is a discrete random variable with ℙ ${{ D_n = k } = {1 over {k(k+1)}} {n over {n-1}}, ; k=1,2,ldots, n-1}$ , which is independent of $(X_2,ldots, X_n)$ . This distributional recursion was not studied previously in the sense of weak convergence. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009" @default.
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• W4240348261 date "2008-08-29" @default.
• W4240348261 modified "2023-10-18" @default.
• W4240348261 title "A limiting distribution for the number of cuts needed to isolate the root of a random recursive tree" @default.
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• W4240348261 doi "https://doi.org/10.1002/rsa.20233" @default.
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