Random Subwords, Pipe Dreams, and Billiards

Let (W,S) be a Coxeter system, and let w be a finite word over the alphabet S. We can randomly and independently delete some of the letters from w and then multiply the resulting subword to get a random element of W. I will explain how to view special cases of this general setup in terms of random pipe dreams or random billiard trajectories. Alternatively, we could multiply the random subword using the Demazure product; this leads to strong connections with integrable probability. I will discuss several results about these random objects, and I will also propose several potential directions for further work. Part of this talk is based on joint work with Pakawut Jiradilok and Elchanan Mossel.

For information about the Richard P. Stanley Seminar in Combinatorics, visit https://math.mit.edu/combin/