Random Transposition Shuffle
نویسندگان
چکیده
Recall that variation distance is defined as ‖μ− ξ‖ = 12 ∑ x∈Ω |μ(x)− ξ(x)| = maxA⊂Ω |μ(A)− ξ(A)|. Recall also that for any t > τmix · dln −1e we have ∆(t) ≤ . In general, our goal was to randomly sample elements of a large set Ω from a distribution defined implicitly by assigning a positive weight w(x) to each x ∈ Ω and then normalizing. So, Pr[x is choosen] = w(x) Z where Z = ∑ x∈Ω w(x). However, Z is in general not known; in fact, often the goal is to compute Z (see the next lecture for examples).
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