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Splitting hairs (with choice)Mathematical Physics & Probability
|Speaker: ||Matt Junge, University of Washington|
|Related Webpage: ||http://www.mathjunge.com/|
|Location: ||1147 MSB|
|Start time: ||Wed, Apr 8 2015, 4:10PM|
Sequentially place n balls into n bins. For each ball, two bins are sampled uniformly and the ball is placed in the emptier of the two. Computer scientists like that this does a much better job of evenly distributing the balls than the "choiceless" version where one places each ball uniformly. Consider the continuous version: Form a random sequence in the unit interval by having the nth term be whichever of two uniformly placed points falls in the larger gap between the previous n-1 points. We confirm the intuition that this sequence is a.s. equidistributed, resolving a conjecture from Itai Benjamini, Pascal Maillard and Elliot Paquette. The history goes back a century to Weyl and more recently to Kakutani.