where σx and σ c,λ=1 i,N L (r s ) are given by Eqs. 35 and 38, respectively. In contrast to Eq. 33, which holds for the σ i vanishing at large N , the i-independent part of the fluctuation function in Eq. 39 is absorbed by the H function since it survives the N → ∞ limit. To obtain σc,λ L (r s ), we equate the r.h.s. of Eq. 38 to the exact w λ=1 (r s ) [Eq. 36; PW92] and numerically solve the resulting equation for σc,λ L (r s ). We use i max = 5000 and this i max value is more than sufficient for r s < 1000 to ensure the convergence of the the σc,λ L solutions. The resulting σc,λ L data are shown in Fig. , and we fit those to: