Theoretical Statistics and Mathematics Unit

Seminar and Colloquium of the week


Title :Shuffling cards by spatial motion
Speaker : Soumik Pal (University of Washington)
Time : September 20, 2017 (Wednesday), 11:15 AM
Venue : Auditorium
Abstract : Shuffling a pack of cards refers to a random process by which the arrangement of the cards in the pack become uniformly distributed over all permutations. The big questions for all such methods are (i) does this method work, and (ii) how long does it take? The answers to these questions can be obtained for many methods of shuffling (e.g., riffle shuffle) to utter precision. However, when there is a spatial effect on shuffling, almost nothing is known in the literature, even though such methods are popular in “real world”. I will discuss a model of card shuffling called "smooshing" where cards, spread as points on a rectangular table, are repeatedly randomly gathered under the palm and then spread across the table. A shuffling or permutation of the cards is then obtained by gathering the cards in a pile by their increasing x-coordinate values. When there are m cards on the table we show that the cards get shuffled in time O(m) with precise constants computed for the diffusion limit. The model has a rather interesting connection with random fluid mixing which is an important area that is virtually unexplored. Based on a joint work with Persi Diaconis.

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