{"id":"openai-math/From-partial-permutation-information-to-Fourier-bounds","pdf":"https://github.com/openai/math/blob/main/preprints/From-partial-permutation-information-to-Fourier-bounds-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/From-partial-permutation-information-to-Fourier-bounds-September-26-2026","tags":["probability","permutations","fourier-analysis"],"score":0,"title":"From partial permutation information to Fourier bounds","domain":"Probability and statistical mechanics","family":"238","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We show how information about partial permutations controls full permutation laws. Let n tend to infinity through multiples of eight. If the images of a uniformly chosen $`7n/8`$ labels approach the uniform injection law in average total variation, and the sign mean tends to zero, then the product of two independent permutations with the given law converges to uniform on S n .","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"}