Spot Topics for Inference and Statistical Physics
A collection of often ignored results, May 2024
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Dall-E2. The exact prompt was “the essence of disordered systems in inference problems, futuristic art”.
Synopsis
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In this document, I collected some interesting results revolving around Statistical Physics that are often taken as granted or briefly overviewed.
Chapter I is a brief introduction to Thermodynamics, one of the fields where the first relevant questions for modern Statistical Physics originated. In Chapter II we collect more formal statements about objects and techniques often used in practice. Emphasis is on those required for replica computations, unfortunately not treated here in detail. In Chapter III we zoom out again, and reinterpret some previously stated results in the context of Information Theory. Thanks to the previous discussions, it will allow us to give further justification towards the fact that all fields have a very wide overlap, obscured by different terminologies, and different questions.