A hierarchical version of the de Finetti and Aldous-Hoover representations

Austin, Tim; Panchenko, Dmitry
August 2014
Probability Theory & Related Fields;Aug2014, Vol. 159 Issue 3/4, p809
Academic Journal
We consider random arrays indexed by the leaves of an infinitary rooted tree of finite depth, with the distribution invariant under the rearrangements that preserve the tree structure. We call such arrays hierarchically exchangeable and prove that they satisfy an analogue of de Finetti's theorem. We also prove a more general result for arrays indexed by several trees, which includes a hierarchical version of the Aldous-Hoover representation.


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