Random Records and Cuttings in Split Trees

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• Cecilia Holmgren (Uppsala University)
• Thursday 12 May 2011, 14:30-15:30
• MR12.

If you have a question about this talk, please contact Andrew Thomason.

I will discuss the asymptotic number of random records in an arbitrary split tree or equivalently, the number of random cuttings required to eliminate the tree. The split trees, introduced by Devroye, form a large class of random trees of logarithmic height. Some important examples are binary search trees, $m$-ary search trees, quadtrees, tries, digital search trees, medians of $(2k+1)$-trees and simplex trees.

I will explain how a classical limit theorem for convergence of sums of triangular arrays to infinitely divisible distributions can be used to determine the distribution of the number of records or cuts. After normalization the distributions are shown to be asymptotically weakly 1-stable.

This talk is part of the Combinatorics Seminar series.

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