{"id":"openai-math/Compatibility-entropy-and-the-spectrum-of-a-Thorp-sweep","pdf":"https://github.com/openai/math/blob/main/preprints/Compatibility-entropy-and-the-spectrum-of-a-Thorp-sweep-September-26-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Compatibility-entropy-and-the-spectrum-of-a-Thorp-sweep-September-26-2026","tags":["probability","random-permutations","markov-chain-mixing"],"score":0,"title":"Compatibility entropy and the spectrum of a Thorp sweep","domain":"Probability and statistical mechanics","family":"238","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove that the Thorp shuffle on $`n=2^d`$ cards mixes in $`\\Theta(d)`$ physical shuffles. After a sufficiently large fixed number of coordinate sweeps, the total-variation distance of the full permutation from uniform tends to zero as $`d\\to\\infty`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-26","reactions":{},"formalized":true,"family_title":"Optimal logarithmic mixing of the Thorp shuffle"}