A Limit Law for the Root Value of Minimax Trees
Tämur Ali Khan, Johann Wolfgang Goethe Universität, Germany
Luc Devroye, McGill University, Canada
Ralph Neininger, Wolfgang Goethe Universität, Germany
Abstract
We consider minimax trees with independent, identically
distributed leaf values that have a continuous distribution function
FV
being strictly increasing on the range where 0< FV <1. It was
shown by Pearl that the root value of such trees
converges to a deterministic limit in probability
without any scaling. We show that after normalization we have
convergence in distribution to a nondegenerate limit random
variable.
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