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

Tim Austin; Dmitry Panchenko

doi:10.1007/s00440-013-0521-0

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

Tim Austin, Dmitry Panchenko

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	809-823
Number of pages	15
Journal	Probability Theory and Related Fields
Volume	159
Issue number	3-4
DOIs	https://doi.org/10.1007/s00440-013-0521-0
State	Published - Aug 2014

Keywords

Exchangeability
Spin glasses

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/s00440-013-0521-0

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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{\textquoteright}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 = "Exchangeability, Spin glasses",

author = "Tim Austin and Dmitry Panchenko",

note = "Funding Information: T. Austin was partially supported by fellowship from Clay Mathematics Institute and D. Panchenko was partially supported by NSF grant. Publisher Copyright: {\textcopyright} 2013, Springer-Verlag Berlin Heidelberg",

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AU - Panchenko, Dmitry

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Y1 - 2014/8

N2 - 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.

AB - 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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KW - Spin glasses

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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