Manuscript Em01-E@2 · Em01-E-v2.tex · section · 54f8f8c2

Cutoffs and profiles

References, profiles, and authorized extensions › Cutoffs and profiles · lines 2277–2299

One-profile convergence does not imply profile independence. For two verified expansions, compare their finite distributions or prove convergence to zero of the difference of their subtracted families.

Under Route C the comparison is explicitly

A_{λ, k}^{ρ} - A_{λ, k}^{ρ} = \frac{1}{k !} H_{λ, J_{λ} - k} [\cdot] (ρ - ρ),

T^{ρ} - T^{ρ} = H_{0, J_{0}} [\cdot] (ρ - ρ),

with the last expression zero when the degree-zero chain is absent. The application proves only its stated factorized-profile result, not independence for arbitrary eight-variable profiles.

Displayed formulas in this passage

unlabeled · line 2285
$A_{λ, k}^{ρ} - A_{λ, k}^{ρ} = \frac{1}{k !} H_{λ, J_{λ} - k} [\cdot] (ρ - ρ),$
unlabeled · line 2291
$T^{ρ} - T^{ρ} = H_{0, J_{0}} [\cdot] (ρ - ρ),$

Nearby in this section

proposition: Proposition: Cutoff locality