On the Golomb-Dickman constant under Ewens sampling (opens in new tab)

arXiv:2603.23175v1 Announce Type: cross Abstract: We define a generalized Golomb-Dickman constant $\lambda_{\theta}$ as the limiting expected proportion of the longest cycle in random permutations under the Ewens measure with parameter $\theta > 0$. Exploiting the independence properties of Kingman's Poisson process construction of the Poisson-Dirichlet distribution, we obtain an explicit integral representation for $\lambda_{\theta}$ in terms of the exponential integral. The dependence of $...