B0751
Title: Yang-Baxter maps and independence preserving property
Authors: Makiko Sasada - The University of Tokyo (Japan) [presenting]
Abstract: A surprising relationship between two properties for bijective functions $F :X \times X \to X \times X$ is discussed for a set $X$, which are introduced from very different backgrounds and seemingly unrelated. One of the properties is that $F$ is a Yang-Baxter map, and the other is the independence preserving property (IP property), which has been used to characterize special probability distributions such as normal, gamma, exponential, beta, etc. Recently, these characterization results have been getting attention in the study of stochastic integrable models and discrete integrable systems. In this context, an explicit class of birational functions $F: \mathbb{R}_+^2 \to \mathbb{R}_+^2$, which originates from the discrete KdV equation, turned out to have these two properties, namely they are (parameter-dependent) Yang-Baxter maps and also have the IP property. This motivates the study of a relationship between the Yang-Baxter maps and the IP property, which has never been studied to best awareness.
