Rigorous results on disordered system: some efforts tounderstand the replica method (Tutorial)

Anton Bovier
Weierstrass Institute, Berlin

I will briefly review the state of rigorous results on the statistical mechanics of disordered systems. I will then give a brief introduction to the formalism of random Gibbs measures and metastates. In the main part of my talk I will examplify these concepts in the context of a large class of exactly solvable mean field models that were introduced by Derrida in the 80's. We will see how in this setting a full 'replica symmetry breaking' solution a la Parisi can be derived rigorously.

Presentation (PDF File)

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