{"id":"openai-math/Conditional-coordinate-sweeps-and-analytic-transfer","pdf":"https://github.com/openai/math/blob/main/preprints/Conditional-coordinate-sweeps-and-analytic-transfer-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Conditional-coordinate-sweeps-and-analytic-transfer-September-26-2026","tags":["probability","random-permutations","markov-chain-mixing"],"score":0,"title":"Conditional coordinate sweeps and analytic transfer","domain":"Probability and statistical mechanics","family":"238","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"For coordinate sweeps with near-uniform line laws and line sizes among powers of two in a suitable fixed interval, we prove a Schatten-moment bound after conditioning on any feasible collection of prescribed card trajectories. An analytic transfer to binary sweeps then shows that a fixed number of sweeps mixes the Thorp shuffle on $`2^d`$ cards in $`O(d)`$ physical steps, matching the order of the support lower bound.","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"}