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Explicit Cutoff Profiles for Colored Top-m-to-Random Shuffles
Probability| Speaker: | Ivan Feng, University of Southern California |
| Location: | zoom |
| Start time: | Thu, Oct 22 2026, 1:10PM |
Description
How long does it take to randomize a deck of colored cards? We study a shuffle that removes the top m cards, randomly reorders and recolors them, and reinserts them uniformly into the deck. I will present explicit cutoff profiles describing the sharp transition to randomness. The proof connects an exact description of the shuffle’s distribution with a Poisson limit for untouched cards.