Theoretical Statistics and Mathematics Unit, ISI 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.