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VOL. 87 | 2021 Discrete integrable systems and Pitman's transformation
David A. Croydon, Makiko Sasada

Editor(s) Yuzuru Inahama, Hirofumi Osada, Tomoyuki Shirai

Abstract

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.

Information

Published: 1 January 2021
First available in Project Euclid: 20 January 2022

Digital Object Identifier: 10.2969/aspm/08710381

Subjects:
Primary: 37K60
Secondary: 37B15 , 37K10 , 37L40 , 60G50 , 82B99

Keywords: Box-Ball System , integrable systems , Invariant measures , KdV equation , Pitman's transformation , Random walks , Toda lattice

Rights: Copyright © 2021 Mathematical Society of Japan

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