A dynamic programming approach to the Parisi functional (Q2802130)
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scientific article; zbMATH DE number 6573161
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A dynamic programming approach to the Parisi functional |
scientific article; zbMATH DE number 6573161 |
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A dynamic programming approach to the Parisi functional (English)
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25 April 2016
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Parisi formula
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Sherrington-Kirkpatrick model
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dynamic programming
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The paper deals with the Parisi functional and its main properties. The Parisi functional is determined by a solution of the Parisi partial differential equation depending on a measure. In the case that the measure has many atoms, the main properties of a solution of the Parisi PDE are well known. In case of the general measure, the question of uniqueness of a solution of the Parisi PDE was open. Using standard arguments from semi-linear parabolic PDEs, the authors prove the existence, uniqueness and regularity of the solution. In this paper, the strict convexity of the Parisi functional is also proved as an application of the properties of the Parisi PDE.
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