Statistically close

The variation distance of two distributions X and Y over a finite domain D , (often referred to as statistical difference or statistical distance in cryptography) is defined as

Δ ( X , Y ) = 1 2 ∑ α ∈ D | Pr [ X = α ] − Pr [ Y = α ] | .

We say that two probability ensembles { X k } k ∈ N and { Y k } k ∈ N are statistically close if Δ ( X k , Y k ) is a negligible function in k .