{"id":"openai-math/Routing-densities-and-representation-contraction-for-Thorp-sweeps","pdf":"https://github.com/openai/math/blob/main/preprints/Routing-densities-and-representation-contraction-for-Thorp-sweeps-September-26-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Routing-densities-and-representation-contraction-for-Thorp-sweeps-September-26-2026","tags":["probability","mixing-times","card-shuffling"],"score":0,"title":"Routing densities and representation contraction for Thorp sweeps","domain":"Probability and statistical mechanics","family":"238","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"For $`N=2^d`$ cards, we prove that an absolute number of coordinate sweeps of the Thorp shuffle brings the full permutation law to total-variation distance tending to zero from uniform. The mixing time therefore has optimal order $`\\Theta(\\log N)`$ in physical shuffles.","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"}