Random overlap structures: properties and applications to SPIN glasses
The authors consider some connections between random probability measures on Hilbert spaces and the Gibbs measures of spin glasses with Gausian disorder. Random overlap structures are random elements on the space of probability measures on the unit ball of a Hilbert space, where two measures are identified if they differ by an isometry. It is proved that the so-called ``cavity mapping'' on the space of random overlap structures is continuous, leading to a proof of the stochastic stability conjecture for the limiting Gibbs measures of a large class of spin glass models.
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