The Interaction Between Multi-Overlaps in the High Temperature Phase of the Sherrington-Kirkpatrick Spin Glass

TL;DR

This paper investigates the joint distribution of multi-overlaps in the high temperature phase of the SK spin glass model, revealing they form a Gaussian process with a specific covariance structure when scaled appropriately.

Contribution

It extends Talagrand's work by characterizing the joint behavior of multiple multi-overlaps as a Gaussian process in the high temperature phase.

Findings

Joint distribution of multi-overlaps is Gaussian

Explicit covariance structure derived

Scaling leads to non-trivial limiting distributions

Abstract

We explore the joint behavior of a finite number of multi-overlaps in the high temperature phase of the SK model. Extending work by M. Talagrand, we show that, when these objects are scaled to have non-trivial limiting distributions, the joint behavior is described by a Gaussian process with an explicit covariance structure.