# Seminar at SMU Delhi

February 19, 2014 (Wednesday) , 3:30 PM at Webinar
Speaker: Arvind Ayyer, IISc Bangalore
Title: Probabilistic Juggling
Abstract of Talk
We consider a juggler who has k balls, can throw up to a maximum height h, and throws each successive ball to a random height subject to the condition that no two balls arrive at the same time. Such Markov chains and their variants were first considered by Warrington in 2005, who found the stationary distribution when the heights were chosen uniformly. We generalize his results by first considering arbitrary height probabilities. Leskela, Varpanen, and Engstrom considered the unbounded height case, which we also generalize. Further, we prove results for the case of infinite number of balls. Lastly, we show that one particular finite state Markov chain converges to its stationary distribution in finite time. This is joint work with Jeremie Bouttier, Sylvie Corteel and Francois Nunzi.