Discrete integrable systems and Pitman's transformation

2020/07/13 by David A. Croydon, Croydon, David A., Makiko Sasada +1 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2007.06206

openalex publication_date 2020/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Soliton decomposition of the Box-Ball System
• Dynamics of the multicolor box-ball system with random initial conditions via Pitman's transformation

Cited by

• Ultra-Discretization of Yang-Baxter Maps, Probability Distributions and Independence Preserving Property

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