You are here

Shuffling cards by spatial motion

Soumik Pal, University of Washington
Monday, April 17, 2017 - 2:30pm to 3:30pm
THO 235

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 where a pack of cards, spread as points on a rectangular table, is subjected to short random motions applied randomly at different spots of 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, in the diffusion limit, the cards get shuffled in time O(m). The model and the analysis are connected to fluid dynamics, reflected diffusions, and random flows of measures. Based on a joint work with Persi Diaconis.

Event Type: 
Event Subcalendar: