离散可积系统与Pitman变换
Discrete integrable systems and Pitman's transformation
AI总结：
本文探讨Pitman变换与多种经典可积系统的关系，包括box-ball系统、超离散和离散KdV方程及超离散和离散Toda晶格方程，揭示其在无限配置下启动可积系统动力学的重要性。
摘要：
本文综述了Pitman变换与多种经典可积系统之间的关系，包括box-ball系统、超离散和离散KdV方程以及超离散和离散Toda晶格方程。阐述了这种联系如何使可积系统的动力学可以从无限配置开始，这对研究不变测度至关重要。在空间独立且相同分布的特殊情况下，也报道了相关进展。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
