Before revision:   then \[E_\alpha^0\left(x_1,\ldots,x_n\right)=e\in T\left(x_1,\ldots,x_n\right) |e|^\alpha\,,\] \[C_1\leq n^{-d-\alpha{d}} E^0_\alpha\left(x_1,\ldots,x_n\right)\leq C_2\,\] with high probability as n\rightarrow \infty.
After revision:   then \[E_\alpha^0\left(x_1,\ldots,x_n\right)=e\in T\left(x_1,\ldots,x_n\right) |e|^\alpha\,,\] then there exist constants 0<C_1\leq C_2 so that\[C_1\leq n^{-d-\alpha{d}} E^0_\alpha\left(x_1,\ldots,x_n\right)\leq C_2\,\] with high probability as n\rightarrow \infty.