A general form of certain mean field models for spin glasses
成果类型：
Article
署名作者：
Talagrand, Michel
署名单位：
Universite Paris Cite; Sorbonne Universite
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-007-0121-y
发表日期：
2009
页码：
97-111
关键词：
摘要：
Given numbers a(ij) >= 0 for 1 <= i < j <= N, and given numbers b(i) >= 0, i <= N, we consider the random Hamiltonian Sigma(i, j <= N) root a(ij)g(ij)sigma(i)sigma(j) + Sigma(i <= N) root b(i)g(i)sigma(i), where g(i), g(ij) denote independent standard normal r.v., and where sigma(i) = +/- 1. We give sufficient conditions on the coefficients a(ij) for the system governed by this Hamiltonian to exhibit high-temperature behavior. There results extend known facts concerning the behavior of the Sherrington-Kirkpatrick model at very high-temperature. In a similar manner we give a general form of the perceptron model.
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