论文标题
离散的集成系统和Pitman的转换
Discrete integrable systems and Pitman's transformation
论文作者
论文摘要
我们调查了最新的工作，该工作将Pitman的转换与各种经典的集成系统相关联，包括Box-Ball System，Ultra-Discrete和Invete KDV方程，以及超差异和离散的TODA晶格方程。它解释了该连接如何使可集成系统的动力学从无限构型启动，这在研究不变措施中很重要。在特殊情况下，在空间独立和相同分布的配置中，也报告了后一个主题的进度。
We survey recent work that relates Pitman's transformation to a variety of classical integrable systems, including the box-ball system, the ultra-discrete and discrete KdV equations, and the ultra-discrete and discrete Toda lattice equations. It is explained how this connection enables the dynamics of the integrable systems to be initiated from infinite configurations, which is important in the study of invariant measures. In the special case of spatially independent and identically distributed configurations, progress on the latter topic is also reported.
