Abstract
In this paper we explore the joint behavior of a finite number of multioverlaps in the high temperature phase of the Sherrington–Kirkpatrick model. Extending the work by Talagrand [Spin Glasses: A Challenge for Mathematicians. Cavity and Mean Field Models, A series of Modern Surveys in Mathematics Vol. 46 (Springer-Verlag, Berlin, 2003)], we show that, when these objects are scaled to have nontrivial limiting distributions, the joint behavior is described by a Gaussian process with an explicit covariance structure.
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