Hamilton-Jacobi equations for finite-rank matrix inference

DOI10.1214/19-AAP1556zbMath1460.82007arXiv1904.05294MaRDI QIDQ2657937

Jean-Christophe Mourrat

Publication date: 18 March 2021

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.05294

zbMATH Keywords

Hamilton-Jacobi equationstatistical inferencespin glass

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Weak solutions to PDEs (35D30) Hamilton-Jacobi equations (35F21)

Related Items (10)

Fluctuation results for multi-species Sherrington-Kirkpatrick model in the replica symmetric regime ⋮ Free energy in multi-species mixed \(p\)-spin spherical models ⋮ Nonconvex interactions in mean-field spin glasses ⋮ Hamilton-Jacobi equations for inference of matrix tensor products ⋮ The Parisi formula is a Hamilton–Jacobi equation in Wasserstein space ⋮ Free energy upper bound for mean-field vector spin glasses ⋮ Mutual information for the sparse stochastic block model ⋮ Free energy of multi-layer generalized linear models ⋮ Statistical inference of finite-rank tensors ⋮ Hamilton-Jacobi equations for nonsymmetric matrix inference

Cites Work

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• The Hamilton-Jacobi equation. A global approach
• Fundamental limits of symmetric low-rank matrix estimation
• Free energy in the Potts spin Glass
• Free energy in the mixed \(p\)-spin models with vector spins
• The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference
• Solutions in the large for multi-dimensional, non-linear partial differential equations of first order

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