On the asymptotics of moments of linear random recurrences

Details On the asymptotics of moments of linear random recurrences On the asymptotics of moments of linear random recurrences

2009-10-20

arxiv.org/abs/0910.3835v2

Theory Stoch. Proc. 2010, Vol. 16(32), p. 106-119

Mathematics

Probability

22 pages, 1 figure

Scientific paper

We propose a new method of analyzing the asymptotics of moments of certain linear random recurrences which is based on the technique of iterative functions. By using the method, we show that the moments of the number of collisions and the absorption time in the Poisson-Dirichlet coalescent behave like the powers of the "log star" function which grows slower than any iteration of the logarithm, and thereby prove a weak law of large numbers. Finally, we discuss merits and limitations of the method and give several examples related to beta coalescents, recursive algorithms and random trees.

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