For the Thorp shuffle on 2^d cards, the full permutation law after 1600d complete shuffles tends to uniform in total variation as d grows, uniformly over initial decks; a support bound requires at least 2d−O(1) shuffles, giving mixing time Θ(d).
For the Thorp shuffle on 2^d cards, the full permutation law after 1600d complete shuffles tends to uniform in total variation as d grows, uniformly over initial decks; a support bound requires at least 2d−O(1) shuffles, giving mixing time Θ(d).
For the Thorp shuffle on 2^d cards, the full permutation law after 1600d complete shuffles tends to uniform in total variation as d grows, uniformly over initial decks; a support bound requires at least 2d−O(1) shuffles, giving mixing time Θ(d).
If correct, establishes the optimal logarithmic order for full-deck mixing on dyadic deck sizes.
Does the Thorp shuffle mix its entire dyadic deck in Θ(log deck size) shuffles?
Publication dates and editorial changes.
Allow optional Google Analytics to help improve AIProofWatch? Privacy details.
