The coefficient-of-variation bound for fast mRNA–microRNA dynamics

Let $\rho_\text{fast}^{\delta,\gamma,p}$ denote the fast-regime distribution and let $\rho_0^{\delta}$ denote the corresponding free-mRNA distribution, with $\mathrm{CV}$ their coefficients of variation. Coefficient-of-variation bound. For any $\delta>1$ and $\gamma,p>0$, one has

$$\mathrm{CV}(\rho_\text{fast}^{\delta,\gamma,p})\leq\mathrm{CV}(\rho_0^{\delta}).$$

This would assert that, outside the asymptotic regimes discussed immediately beforehand, binding and production of microRNA do not increase the coefficient of variation relative to free mRNAs. The source presents it as the theoretical result one would like to have; no proof or resolution is supplied here.