Jeffery Kuan (Harvard)

Title: Markov Chains on Partitions

Abstract: We review a family of Markov chains on partitions introduced by A. Borodin and P. Ferrari. These Markov chains are an exactly solvable model in the Anisotropic Kardar-Parisi-Zhang universality class in 2+1 dimensions. We construct these Markov chains in three different ways, all of which involve the representation theory of the unitary group. The first uses representations of the infinite-dimensional unitary group, the second uses the Littlewood-Richardson coefficients describing the decomposition of tensor products of representations, and the third uses a quantum random walk on the dual of the unitary group.