Cutoff for Biased Transpositions in Card Shuffling

Explore the mathematical intricacies of card shuffling in this 47-minute lecture presented by Evita Nestoridi from SUNY Stony Brook at IPAM's Statistical Mechanics Beyond 2D Workshop. Delve into the concept of biased transpositions, building upon the foundational work of Diaconis and Shahshahani on random transpositions. Examine a scenario where cards in the top half of the deck are selected with different probabilities, and discover how this affects the number of steps required for the deck to mix. Learn about the joint work-in-progress with A. Yan, which demonstrates that this biased shuffle takes (2b)−1nlogn steps to mix. Gain insights into the application of statistical mechanics principles to card shuffling algorithms and understand how previous results on random transpositions contribute to this new analysis.