3 problems

Let $U_n(f)$ be the classical $U$-statistic, and let $U_n^\circ(f)$ and the alternating $U$-statistics be the variants considered in the paper. In the degenerate cases, consider th…

Consider the unbalanced triangular Pólya urns described in the surrounding discussion, including the class of more typical unbalanced triangular urns for which the almost-sure limi…

Let ${\mathcal T}_n$ be the conditioned simply generated tree, let $\widehat{{\mathcal T}}$ be its limiting size-biased tree, and let $l_k(T)$ denote the number of vertices at dist…