Geodesic
Multivariate normal limit laws for the numbers of fringe subtrees in \(m\)-ary search trees and preferential attachment trees
Cecilia Holmgren1 ; Svante Janson1 ; Matas Sileikis2
1Uppsala University
2Charles University in Prague
The electronic journal of combinatorics, Tome 24 (2017) no. 2
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We study fringe subtrees of random $m$-ary search trees and of preferential attachment trees, by putting them in the context of generalised Pólya urns. In particular we show that for the random $m$-ary search trees with $ m\leq 26 $ and for the linear preferential attachment trees, the number of fringe subtrees that are isomorphic to an arbitrary fixed tree $ T $ converges to a normal distribution; more generally, we also prove multivariate normal distribution results for random vectors of such numbers for different fringe subtrees. Furthermore, we show that the number of protected nodes in random $m$-ary search trees for $m\leq 26$ has asymptotically a normal distribution.
DOI : 10.37236/6374
Classification : 60C05, 05C05, 05C80, 60F05, 68P05, 68P10
Mots-clés : random trees, fringe trees, normal limit laws, Pólya urns, \(m\)-ary search trees, preferential attachment trees, protected nodes

Cecilia Holmgren  1   ; Svante Janson  1   ; Matas Sileikis  2

1 Uppsala University
2 Charles University in Prague 
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     author = {Cecilia Holmgren and Svante Janson and Matas Sileikis},
     title = {Multivariate normal limit laws for the numbers of fringe subtrees in \(m\)-ary search trees and preferential attachment trees},
     journal = {The electronic journal of combinatorics},
     year = {2017},
     volume = {24},
     number = {2},
     doi = {10.37236/6374},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/6374/}
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Cecilia Holmgren; Svante Janson; Matas Sileikis. Multivariate normal limit laws for the numbers of fringe subtrees in \(m\)-ary search trees and preferential attachment trees. The electronic journal of combinatorics, Tome 24 (2017) no. 2. doi: 10.37236/6374

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