{"id":"openai-math/Conditional-information-under-deterministic-coordinate-sweeps","pdf":"https://github.com/openai/math/blob/main/preprints/Conditional-information-under-deterministic-coordinate-sweeps-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Conditional-information-under-deterministic-coordinate-sweeps-September-26-2026","tags":["probability","random-permutations","information-theory"],"score":0,"title":"Conditional information under deterministic coordinate sweeps","domain":"Probability and statistical mechanics","family":"238","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We bound the information remaining after paths of specified cards in the Thorp shuffle on $`n=2^d`$ cards have been observed. After a fixed number of deterministic coordinate sweeps, the joint endpoint law of further cards is close to uniform on the available positions, on average over the observed paths, provided a fixed positive fraction of labels lies outside both lists. Combined with a Fourier transfer, these bounds give full-deck mixing after $`2048d`$ 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"}