Athreya, Jayadev S.; Fidkowski, Lukasz M. Number theory, balls in boxes, and the asymptotic uniqueness of maximal discrete order statistics. (English) Zbl 1070.60501 Integers 0, Paper A03, 5 p. (2000). Summary: We investigate the asymptotic uniqueness of the maximal order statistic of \(X_1,X_2,\dots,X_n\), i.i.d. positive integer random variables, by casting the problem in a balls-in-boxes setting. We give a necessary and sufficient condition on the distribution of the \(X_i\)’s for the convergence of the probability of uniqueness as \(n\to\infty\). We describe the connection to an interesting problem in number theory. The main techniques used are altering the sample to have random size, specifically, Poisson(\(n\)), and Karamata’s Tauberian theorem. Cited in 2 Documents MSC: 60G70 Extreme value theory; extremal stochastic processes 11K31 Special sequences 60C05 Combinatorial probability 60F05 Central limit and other weak theorems PDFBibTeX XMLCite \textit{J. S. Athreya} and \textit{L. M. Fidkowski}, Integers 0, Paper A03, 5 p. (2000; Zbl 1070.60501) Full Text: EuDML