Optimal logarithmic mixing of the Thorp shuffle
What the paper claims, in its own words
Proves that the Thorp shuffle randomizes labeled cards in physical shuffles, settling its optimal mixing order for power-of-two deck sizes. Convergence is in total variation from the worst initial ordering and concerns the entire permutation, not just individual card positions.
The plain-language explainer for this entry is still coming.
The original papers (12)
- Optimal-order mixing of the Thorp shuffle (PDF, opens in a new tab) September 26, 2026
- Random coordinate frames and partial permutation laws (PDF, opens in a new tab) September 26, 2026
- From partial permutation information to Fourier bounds (PDF, opens in a new tab) September 26, 2026
- Conditional information under deterministic coordinate sweeps (PDF, opens in a new tab) September 26, 2026
- Conditional permutations in a revealed switching environment (PDF, opens in a new tab) September 26, 2026
- Routing densities and representation contraction for Thorp sweeps (PDF, opens in a new tab) September 26, 2026 Formal proof listed
- Row–column symmetry and contraction of coordinate sweeps (PDF, opens in a new tab) September 26, 2026
- Random-subspace tests and trace smoothing for coordinate sweeps (PDF, opens in a new tab) September 26, 2026
- Compatibility entropy and the spectrum of a Thorp sweep (PDF, opens in a new tab) September 26, 2026 Formal proof listed
- Signed tensor densities and diagram budgets for the Thorp shuffle (PDF, opens in a new tab) September 26, 2026
- Conditional coordinate sweeps and analytic transfer (PDF, opens in a new tab) September 26, 2026 Formal proof listed
- A strict four-row permanent inequality and permutation moments (PDF, opens in a new tab) September 26, 2026