Decomposition of mean-field gibbs distributions into product measures

Ronen Eldan, Renan Gross

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number35
Number of pages24
JournalElectronic Journal of Probability
StatePublished - Apr 2018


  • Gaussian width
  • Gibbs distribution
  • Ising model
  • Large deviation
  • Mean field
  • Sparse random graphs

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Decomposition of mean-field gibbs distributions into product measures'. Together they form a unique fingerprint.

Cite this