Before revision:  We show that an \varepsilon_0-locally differentially private algorithm, under shuffling with n users, amplifies to a (\Theta ((1-e^{-\varepsilon_0})\frac{e^{\varepsilon_0\log(1/\delta)}{n}}), \delta) -central differential privacy guarantee .
After revision:  We show that random shuffling of n data records that are input to \varepsilon_0-differentially private local randomizers results in an (O ((1-e^{-\varepsilon_0})\frac{e^{\varepsilon_0\log(1/\delta)}{n}}), \delta) -central differential privacy guarantee .