For the mechanism as implemented over the discrete atoms \(\lbrace  y^{(l)} \rbrace _{l=1}^\ell \) , [1]} show that:
\(\operatorname{\mathbb {P}}\left( \left\Vert L_X(Y)\right\Vert  \ge \varepsilon \mid Y \in \lbrace  y^{(l)} \rbrace _{l=1}^\ell \right) \le \exp \left( -\frac{\epsilon }{2 \Delta _L} \left( \varepsilon - \frac{2 \Delta _L}{\epsilon } \log (\ell ) \right) \right)\) 

Для механизма, реализованного на дискретных атомах \(\lbrace  y^{(l)} \rbrace _{l=1}^\ell \), [1] показывает, что:

\(\operatorname{\mathbb {P}}\left( \left\Vert L_X(Y)\right\Vert  \ge \varepsilon \mid Y \in \lbrace  y^{(l)} \rbrace _{l=1}^\ell \right) \le \exp \left( -\frac{\epsilon }{2 \Delta _L} \left( \varepsilon - \frac{2 \Delta _L}{\epsilon } \log (\ell ) \right) \right)\)