We study Galton-Watson branching processes conditioned on the total progeny to be n which are scaled by a sequence cn tending to infinity as o( √ n). It is shown that this proce...
We establish the asymptotic normality of the number of upper records in a sequence of iid geometric random variables. Large deviations and local limit theorems as well as approxim...
A periodic tree Tn consists of full n-level copies of a finite tree T. The tree Tn is labeled by random bits. The root label is chosen randomly, and the probability of two adjace...
Let Un,p be the random unary predicate and Tk the almost sure first-order theory of Un,p under the linear ordering, where k is a positive integer and n−1/k p(n) n−1/(k+1) . F...