On the Dovbysh-Sudakov representation result
Dmitry Panchenko
TL;DR
This paper provides a detailed proof of the Dovbysh-Sudakov representation for Gram-de Finetti matrices, building on Aldous and Hoover's work on symmetric weakly exchangeable arrays, emphasizing positive definiteness.
Contribution
It offers a comprehensive proof of the Dovbysh-Sudakov representation specifically for positive definite Gram-de Finetti matrices, extending previous general results.
Findings
Detailed proof of the Dovbysh-Sudakov representation
Clarification of the structure of Gram-de Finetti matrices
Extension of Aldous and Hoover's representation results
Abstract
We present a detailed proof of the Dovbysh-Sudakov representation for symmetric positive definite weakly exchangeable infinite random arrays, called Gram-de Finetti matrices, which is based on the representation result of Aldous and Hoover for arbitrary (not necessarily positive definite) symmetric weakly exchangeable arrays.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Random Matrices and Applications · Theoretical and Computational Physics