{"id":"openai-math/Random-subspace-tests-and-trace-smoothing-for-coordinate-sweeps","pdf":"https://github.com/openai/math/blob/main/preprints/Random-subspace-tests-and-trace-smoothing-for-coordinate-sweeps-September-26-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Random-subspace-tests-and-trace-smoothing-for-coordinate-sweeps-September-26-2026","tags":["probability","mixing-times","card-shuffling","combinatorics"],"score":0,"title":"Random-subspace tests and trace smoothing for coordinate sweeps","domain":"Probability and statistical mechanics","family":"238","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove that an absolute number of coordinate sweeps of the Thorp shuffle on $`n=2^d`$ positions brings the full permutation to total-variation distance at most $`\\frac12n^{-5}`$ from uniform, uniformly over the initial deck. Thus $`O(d)`$ physical shuffles suffice, which is optimal in order.","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"}