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Local extrema in random trees

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  • Lane Clark

Abstract

The number of local maxima (resp., local minima) in a tree T ∈ 𝒯 n rooted at r ∈ [ n ] is denoted by M r ( T ) (resp., by m r ( T ) ). We find exact formulas as rational functions of n for the expectation and variance of M 1 (T) and m n ( T ) when T ∈ 𝒯 n is chosen randomly according to a uniform distribution. As a consequence, a.a.s. M 1 ( T ) and m n ( T ) belong to a relatively small interval when T ∈ 𝒯 n .

Suggested Citation

  • Lane Clark, 2005. "Local extrema in random trees," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-16, January.
    • Handle: RePEc:hin:jijmms:489450
    DOI: 10.1155/IJMMS.2005.3867
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