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Signed tensor densities and diagram budgets for the Thorp shuffle

OpenAI

OpenAI Mathopenai-math/Signed-tensor-densities-and-diagram-budgets-for-coordinate-sweepsSep 26, 2026math.PRAI-generatedscore 0

We prove that a fixed number of coordinate sweeps of the Thorp shuffle on $2^d$ cards makes the squared L 2 distance of the full permutation density from uniform tend to zero as $d\to\infty$. In particular, the total-variation mixing time is $\Theta(d)$ physical shuffles.

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