Intersecting random half-spaces: Toward the Gardner-Derrida formula.

DOI10.1214/aop/1019160259zbMath1043.82030OpenAlexW1540698682MaRDI QIDQ1872142

Michel Talagrand

Publication date: 6 May 2003

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

Full work available at URL: https://doi.org/10.1214/aop/1019160259

zbMATH Keywords

spin glassesperceptroncavity methodreplica-symmetric formula

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) 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) Stochastic processes (60G99) Neural nets applied to problems in time-dependent statistical mechanics (82C32) Limit theorems in probability theory (60F99)

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Cites Work

• Une inegalité du type de Slepian et Gordon sur les processus gaussiens. (An inequality of Slepian and Gordon type for Gaussian processes)
• Huge random structures and mean field models for spin glasses
• The Sherrington-Kirkpatrick model: A challenge for mathematicians
• Rigorous results for the Hopfield model with many patterns
• Neural networks and physical systems with emergent collective computational abilities.