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We propose a conjecture for the limit of mean-field spin glasses with a bipartite structure, and show that the conjectured limit is an upper bound.
Parisi’s formula is a Hamilton-Jacobi equation in Wasserstein space
J.-C. Mourrat · 1906
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Positive definite functions on spheres
I. J. Schoenberg · 1942
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Generalized solutions of non-linear equations of first order
E. Hopf · 1965
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Infinite number of order parameters for spin-glasses
G. Parisi · 1979
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A sequence of approximated solutions to the SK model for spin glasses
G. Parisi · 1980
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On Hopf’s formulas for solutions of Hamilton-Jacobi equations
M. Bardi and L. C. Evans · 1984
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Hamilton-Jacobi equations in infinite dimensions. I. Uniqueness of viscosity solutions
M. G. Crandall and P.-L. Lions · 1985
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Spin glass in an lsing two-sublattice magnet
I. Y. Korenblit and E. Shender · 1985
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Hamilton-Jacobi equations in infinite dimensions. II. Existence of viscosity solutions
M. G. Crandall and P.-L. Lions · 1986
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Hamilton-Jacobi equations in infinite dimensions. III
M. G. Crandall and P.-L. Lions · 1986
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Hopf formula and multitime Hamilton-Jacobi equations
P.-L. Lions and J.-C. Rochet · 1986
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Antiferromagnetic ising spin glass
Y. V. Fyodorov, I. Y. Korenblit, and E. Shender · 1987
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Phase transitions in frustrated metamagnets
Y. V. Fyodorov, I. Y. Korenblit, and E. Shender · 1987
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Spin glass theory and beyond: an introduction to the replica method and its applications
M. Mézard, G. Parisi, and M. Virasoro · 1987
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On oblique derivative problems for fully nonlinear second-order elliptic PDEs on domains with corners
P. Dupuis and H. Ishii · 1991
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User’s guide to viscosity solutions of second order partial differential equations
M. G. Crandall, H. Ishii, and P.-L. Lions · 1992
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Sum rules for the free energy in the mean field spin glass model
F. Guerra · 2001
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Broken replica symmetry bounds in the mean field spin glass model
F. Guerra · 2003
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Free energy in the generalized Sherrington-Kirkpatrick mean field model
D. Panchenko · 2005
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Information-theoretic limits for the matrix tensor product, Preprint, arXiv:2005.11273
G. Reeves · 2005
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Hamilton-Jacobi equations for nonsymmetric matrix inference
H.-B. Chen · 2006
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Large deviations for stochastic processes
J. Feng and T. G. Kurtz · 2006
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Free energy of the spherical mean field model
M. Talagrand · 2006
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The Parisi formula
M. Talagrand · 2006
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Mean field models for spin glasses. Volume II
M. Talagrand · 2011
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Notes on the p-spin glass studied via Hamilton-Jacobi and smooth-cavity techniques
E. Agliari, A. Barra, R. Burioni, and A. Di Biasio · 2012
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A differential game with a blind player
P. Cardaliaguet and A. Souquière · 2012
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An introduction to the theory of viscosity solutions for first-order Hamilton-Jacobi equations and applications
G. Barles · 2013
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Mean field spin glasses treated with PDE techniques
A. Barra, G. Del Ferraro, and D. Tantari · 2013
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The Parisi ultrametricity conjecture
D. Panchenko · 2013
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Mean field models for spin glasses: some obnoxious problems
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Deterministic differential games under probability knowledge of initial condition
P. Cardaliaguet and M. Quincampoix · 2008
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Hamilton-Jacobi equations in the Wasserstein space
W. Gangbo, T. Nguyen, and A. Tudorascu · 2008
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The Aizenman-Sims-Starr and Guerra’s schemes for the SK model with multidimensional spins
A. Bovier and A. Klimovsky · 2009
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Hamilton-Jacobi equations for inference of matrix tensor products
H.-B. Chen and J. Xia · 2009
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A comparison principle for Hamilton-Jacobi equations related to controlled gradient flows in infinite dimensions
J. Feng and M. Katsoulakis · 2009
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The Sherrington-Kirkpatrick model
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On a class of first order Hamilton-Jacobi equations in metric spaces
L. Ambrosio and J. Feng · 2014
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Free energy and complexity of spherical bipartite models
A. Auffinger and W.-K. Chen · 2014
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Optimal transport and large number of particles
W. Gangbo and A. Świȩch · 2014
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The Parisi formula has a unique minimizer
A. Auffinger and W.-K. Chen · 2015
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Multi-species mean field spin glasses. Rigorous results
A. Barra, P. Contucci, E. Mingione, and D. Tantari · 2015
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The free energy in a multi-species Sherrington-Kirkpatrick model
D. Panchenko · 2015
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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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Free energy in the Potts spin glass
D. Panchenko · 2018
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Free energy in the mixed
D. Panchenko · 2018
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Extending the Parisi formula along a Hamilton-Jacobi equation
J.-C. Mourrat and D. Panchenko · 2020
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