Operator Norm Bounds on the Correlation Matrix of the SK Model at High Temperature

Christian Brennecke, Changji Xu, Horng-Tzer Yau

We prove that the two point correlation matrix $\text{M}=(⟨\ddot{I}{ƒ}_i;\ddot{I}{ƒ}_j⟩{)}_{1\le i,j\le N}\in {\mathbb{R}}^{N\times N}$ of the Sherrington-Kirkpatrick model has the…