Speaker: Guangqu Zheng (Kansas)
Title: Chaos expansion and intransitivity of Gaussian dice
Abstract: : This talk begins with a quick introduction to Wiener chaos expansion and illustrate how one can re-derive Newton’s identity (1676) and Ramanujan’s identity (1912) about $\pi$ using the expansion of two simple functions. The rest of the talk is devoted to the intransitivity of Gaussian dice: We say the n-sided die $(a_1, …, a_n)$ beats $(b_1, …, b_n)$ if a uniformly random face of $a$ has greater value than a random face of $b$. The intransitivity occurs when “beats” relation on the set of dice cannot be extended to a linear order. Our talk will focus on the case of Gaussian faces and is partially based on a recent joint work with J. Hązła, E. Mossel and Nathan Ross (arXiv:1804.00394), which was motivated by the Polymath project 13.