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2018 Decomposition of mean-field Gibbs distributions into product measures
Ronen Eldan, Renan Gross
Electron. J. Probab. 23: 1-24 (2018). DOI: 10.1214/18-EJP159


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.


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Ronen Eldan. Renan Gross. "Decomposition of mean-field Gibbs distributions into product measures." Electron. J. Probab. 23 1 - 24, 2018.


Received: 15 September 2017; Accepted: 20 March 2018; Published: 2018
First available in Project Euclid: 28 April 2018

zbMATH: 1390.60346
MathSciNet: MR3798245
Digital Object Identifier: 10.1214/18-EJP159

Primary: 05C80 , 60F10 , 60K35 , 82B20

Keywords: Gaussian width , Gibbs distribution , Ising model , large deviation , Mean field , sparse random graphs


Vol.23 • 2018
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