The degree Gini index of several classes of random trees and their poissonized counterparts—Evidence for duality
Published in Journal of Stochastic Analysis, 2022
Recommended citation: Domicolo, C., Zhang, P. and Mahmoud, H. (2022). "The degree Gini index of several classes of random trees and their poissonized counterparts---Evidence for duality." Journal of Stochastic Analysis, 3(4), 1. https://doi.org/10.31390/josa.3.4.01
There is an unproven duality theory hypothesizing that random discrete trees and their poissonized embeddings in continuous time share fundamental properties. We give additional evidence in favor of this theory by showing that several classes of random trees growing in discrete time and their poissonized counterparts have the same limiting degree Gini index. The classes that we consider include binary search trees, binary pyramids and random caterpillars.