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We consider ferromagnetic spin models on dilute random graphs and prove that, with suitable one-body infinitesimal perturbations added to the Hamiltonian, the multi-overlaps concentrate for all temperatures, both with respect to the thermal Gibbs average and the quenched randomness.
Spin glass theory and beyond
M. Mézard, G. Parisi, and M.-A. Virasoro · 1987
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Absence of self-averaging of the order parameter in the sherrington-kirkpatrick model
L. A. Pastur and M. V. Shcherbina · 1991
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More about absence of selfaverageness of the order parameter in the sherrington-kirkpatrick model
M. V. Shcherbina · 1991
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General properties of overlap probability distributions in disordered spin systems. towards parisi ultrametricity
S. Ghirlanda and F. Guerra · 1998
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On the stability of the quenched state in mean-field spin-glass models
M. Aizenman and P. Contucci · 1998
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Replica bounds for diluted non-poissonian spin systems
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Extended variational principle for the Sherrington-Kirkpatrick spin-glass model
M. Aizenman, R. Sims, and S. L. Starr · 2003
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Replica bounds for optimization problems and diluted spin systems
S. Franz and M. Leone · 2003
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Bounds for diluted mean-fields spin glass models
D. Panchenko and M. Talagrand · 2004
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F. Guerra · 2005
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An introduction to mean field spin glass theory: Methods and results
F. Guerra · 2006
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Overlap fluctuations from the boltzmann random overlap structure
A. Barra and L. De Sanctis · 2006
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Stability properties and probability distributions of multi-overlaps in dilute spin glasses
A. Barra and L. De Sanctis · 2007
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Estimating random variables from random sparse observations
A. Montanari · 2008
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Self-averaging identities for random spin systems
L. De Sanctis and S. Franz · 2009
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Sharp bounds for optimal decoding of low-density parity-check codes
S. Kudekar and N. Macris · 2009
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Mean field models for spin glasses: Volume I: Basic examples
M. Talagrand · 2010
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The Sherrington-Kirkpatrick Model
D. Panchenko · 2013
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Superconcentration and Related Topics
S. Chatterjee · 2014
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Absence of replica symmetry breaking in the random field ising model
S. Chatterjee · 2015
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The interpolation method for random graphs with prescribed degrees
J. Salez · 2016
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The Layered Structure of Tensor Estimation and its Mutual Information
J. Barbier, N. Macris, and L. Miolane · 2017
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Community detection and stochastic block models
E. Abbe · 2018
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T. E. Harris’ contributions to interacting particle systems and percolation
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F. Guerra · 2012
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