Geodesic
Tail Bounds for the Wiener Index of Random Trees
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07), DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07) (2007).

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Upper and lower bounds for the tail probabilities of the Wiener index of random binary search trees are given. For upper bounds the moment generating function of the vector of Wiener index and internal path length is estimated. For the lower bounds a tree class with sufficiently large probability and atypically large Wiener index is constructed. The methods are also applicable to related random search trees. 
@article{DMTCS_2007_special_253_a6,
     author = {Khan, T\"amur Ali and Neininger, Ralph},
     title = {Tail {Bounds} for the {Wiener} {Index} of {Random} {Trees}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07)},
     year = {2007},
     doi = {10.46298/dmtcs.3524},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3524/}
}
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Khan, Tämur Ali; Neininger, Ralph. Tail Bounds for the Wiener Index of Random Trees. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07), DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07) (2007). doi : 10.46298/dmtcs.3524. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3524/

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