Decomposition of mean-field Gibbs distributions into product measures

作者：Eldan Ronen^*; Gross Renan

来源：Electronic Journal of Probability, 2018, 23(0): 35.

DOI：10.1214/18-EJP159

• mean field
• large deviation
• Gibbs distribution
• Ising model
• Gaussian width
• sparse random graphs

We show that under a low complexity condition on the gradient of a Hamiltonian, Gibbs distributions on the Boolean hypercube are approximate mixtures of product measures whose probability vectors are critical points of an associated mean-field functional. This extends a previous work by the first author. As an application, we demonstrate how this framework helps characterize both Ising models satisfying a mean-field condition and the conditional distributions which arise in the emerging theory of nonlinear large deviations, both in the dense case and in the polynomially-sparse case.

• 出版日期2018