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نویسنده
چکیده
For a martingale (Xn) converging almost surely to a random variable X , the sequence (Xn − X) is called martingale tail sum. Recently, Neininger [Random Structures Algorithms, 46 (2015), 346-361] proved a central limit theorem for the martingale tail sum of Régnier’s martingale for the path length in random binary search trees. Grübel and Kabluchko [2014, preprint, arXiv 1410.0469] gave an alternative proof also conjecturing a corresponding law of the iterated logarithm. We prove the central limit theorem with convergence of higher moments and the law of the iterated logarithm for a family of trees containing binary search trees, recursive trees and plane-oriented recursive trees. AMS 2010 subject classifications. Primary 60F15, 68P05; secondary 60F05, 60G42.
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