{"id":"openai-math/Signed-tensor-densities-and-diagram-budgets-for-coordinate-sweeps","pdf":"https://github.com/openai/math/blob/main/preprints/Signed-tensor-densities-and-diagram-budgets-for-coordinate-sweeps-September-26-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Signed-tensor-densities-and-diagram-budgets-for-coordinate-sweeps-September-26-2026","tags":["probability","card-shuffling","markov-chains","mixing-times"],"score":0,"title":"Signed tensor densities and diagram budgets for the Thorp shuffle","domain":"Probability and statistical mechanics","family":"238","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-26","reactions":{},"formalized":false,"family_title":"Optimal logarithmic mixing of the Thorp shuffle"}