A hierarchical version of the de Finetti and Aldous-Hoover representations
Probability
2014-08-05 v4
Abstract
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.
Keywords
Cite
@article{arxiv.1301.1259,
title = {A hierarchical version of the de Finetti and Aldous-Hoover representations},
author = {Tim Austin and Dmitry Panchenko},
journal= {arXiv preprint arXiv:1301.1259},
year = {2014}
}
Comments
v2: new coauthor and new proof of a more general result; v4: some minor changes