منابع مشابه
Charting the Replica Symmetric Phase
Random graph models and associated inference problems such as the stochastic block model play an eminent role in computer science, discrete mathematics and statistics. Based on nonrigorous arguments physicists predicted the existence of a generic phase transition that separates a “replica symmetric phase” where statistical inference is impossible from a phase where the detection of the “ground ...
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Random constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark instances for algorithms and they have been harnessed in probabilistic constructions of combinatorial structures with peculiar features. In an important contribution [Krzakala et al., PNAS 2007] physicists made several predictions on the precise l...
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We study the finite dimensional marginals of the Gibbs measure in the Hopfield model at low temperature when the number of patterns, M , is proportional to the volume with a sufficiently small proportionality constant α > 0. It is shown that even when a single pattern is selected (by a magnetic field or by conditioning), the marginals do not converge almost surely, but only in law. The correspo...
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In this paper we translate Talagrand’s solution of the K-sat model at high temperature into the language of asymptotic Gibbs measures. Using exact cavity equations in the infinite volume limit allows us to remove many technicalities of the inductions on the system size, which clarifies the main ideas of the proof. This approach also yields a larger region of parameters where the system is in a ...
متن کاملThe Replica Symmetric Approximation of the Analogical Neural Network
In this paper we continue our investigation of the analogical neural network, by introducing and studying its replica symmetric approximation in the absence of external fields. Bridging the neural network to a bipartite spin-glass, we introduce and apply a new interpolation scheme to its free energy, that naturally extends the interpolation via cavity fields or stochastic perturbations from the...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2018
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-018-3096-x