The parisi formula

By Michel Talagrand. 2006

637 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Materials Chemistry, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c712dc048d5f1593027e01cb55cbbaf8505e222a

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In Condensed Matter Physics

In Materials Chemistry

In Mathematical Physics

Citations in the corpus

Mean-field inference methods for neural networks (2019, methodology): “ have Gaussian i.i.d. entries. In this case, rigorous 24 5.2 Algorithms and free energies beyond i.i.d. matrices proofs of asymptotic exactness of the mean-ﬁeld solutions were found, for the SK model [Tal06] and the GLM [RP16,BKM+18]. Mean-ﬁeld inference with diﬀerent weight statistics is a priori f”
Free energy of the spherical mean field model (2006, methodology): “Some understanding of the most famous model, the Sherrington-Kirkpatrick model, has recently been gained [ 6 ], and the purpose of the present work is to extend the results of [6] and [7] to the case of the spherical model.”
The complexity of spherical p-spin models - a second moment approach (2015, background): “The formula expresses F (β) through an intricate variational problem, which is greatly simplified when one-step replica symmetry breaking (1-RSB) is known to occur (see [Tal06b] for a definition of this terminology).”
Cleaning large correlation matrices: tools from random matrix theory (2016, background): “[46, 86] or [89] and references therein for a mathematical formalism.”
An Iterative Construction of Solutions of the TAP Equations for the Sherrington–Kirkpatrick Model (2012, methodology): “Ledoux, M., Talagrand, M.: Probability in Banach Spaces.”
The Parisi formula for mixed $p$-spin models (2011, methodology): “ measure of the model, one of them being the ultrametricity of its support. The Parisi formula for the free energy in the Sherrington–Kirkpatrick and mixed p-spin models was proved by M. Talagrand in [24] following the discovery of the replica symmetry breaking interpolation scheme by F. Guerra in [”
The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference (2018, methodology): “In this respect one of the most important tools is the invention of the interpolation method by Guerra and Toninelli [6, 7] which eventually led Talagrand to a remarkable proof [8] of the Parisi formula [9] for the free energy of the Sherrington-Kirkpatrick model [10].”
Rademacher complexity and spin glasses: A link between the replica and statistical theories of learning (2019, background): “1, and we also refer the reader to the relevant literature in physics ([18, 26, 8, 27, 14]) and in mathematics ([17, 23, 28, 29, 30]).”
Polar Codes for Channel and Source Coding (2009, methodology): “Talagrand [110] extended the technique in an intelligent way to obtain lower bounds as well and thus proving the long standing conjecture of Parisi.”
The Parisi ultrametricity conjecture (2011, background): “Talagrand in [18] following the breakthrough invention of the replica symmetry breaking interpolation scheme by F.”