Assuming equilibrium (and thus time invariance of the ensemble) and averaging over all sites in the sample gives a simpler expression for the equal-position correlation function as for the equal-time correlation function: C ( τ τ ) = ⟨ ⟨ s 1 ( 0 ) ⋅ ⋅ s 2 ( τ τ ) ⟩ ⟩ − − ⟨ ⟨ s 1 ( 0 ) ⟩ ⟩ ⟨ ⟨ s 2 ( τ τ ) ⟩ ⟩ .