A Limit Law for the Root Value of Minimax Trees
Tämur Ali Khan, Luc Devroye, Ralph Neininger · Electronic Communications in Probability · 2005
We consider minimax trees with independent, identically distributed leaf values that have a continuous distribution function $F_V$ being strictly increasing on the range where $0 < F_V < 1$. 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.