Discrete integrable systems and Pitman's transformation
Probability
2026-04-15 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2007.06206,
title = {Discrete integrable systems and Pitman's transformation},
author = {David A. Croydon and Makiko Sasada},
journal= {arXiv preprint arXiv:2007.06206},
year = {2026}
}