Exchangeable random measures

Abstraction: Representation theorem for permutation-invariant random measures on array spaces

Key points:

• Studies random measures on A^{N^(k)} (A-valued arrays indexed by size-k subsets of N) whose laws are invariant under permutations of N
• Main result: a representation theorem for such exchangeable random measures, proved using classical results of de Finetti, Hoover, Aldous, and Kallenberg
• Application 1: short new proof of the Dovbysh-Sudakov Representation Theorem for exchangeable positive semi-definite matrices
• Application 2: natural class of limit objects for dilute mean-field spin glass models, retaining more information than the limiting Gram-de Finetti matrix used in Sherrington-Kirkpatrick analysis
• By Tim Austin (2013), arXiv:1302.2116

Connections: Tim Austin · Exchangeability · Random Measure · Spin Glass

Source: http://arxiv.org/abs/1302.2116