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There is an unproven duality theory hypothesizing that random discrete treesand their poissonized embeddings in continuous time share fundamentalproperties. We give additional evidence in favor of this theory by showing thatseveral classes of random trees growing in discrete time and their poissonizedcounterparts have the same limiting degree Gini index. The classes that weconsider include binary search trees, binary pyramids and random caterpillars.

The degree Gini index of several classes of random trees and their poissonized counterparts---an evidence for a duality theory