## FANDOM

567 Pages

Let the statistical difference[1] between two distributions $X$ and $Y$ be defined as

$\Delta(X,Y)=\frac{1}{2} \sum _a | \Pr[X=\alpha] - \Pr[Y=\alpha] |$.

We say that two probability ensembles $\{X_k\}_{k\in\N}$ and $\{Y_k\}_{k\in\N}$ are statistically close if $\Delta(X_k,Y_k)$ is a negligible function in $k$.

Statistical difference is based on the L1 norm.

## ReferencesEdit

1. Amit Sahai, Salil P. Vadhan: A complete problem for statistical zero knowledge. J. ACM 50(2): 196-249 (2003)