18.03.2026
Makiko Sasada, University of Tokyo
" Independence Preserving Property in Integrable Systems and Ultra-discretization"
Abstract: The independence preserving (IP) property has long been studied in probability theory, and it has recently been recognized to play an important role in the analysis of stationary distributions of certain integrable systems. In this talk, we first review connections between the IP property and integrable systems, including both classical and stochastic integrable systems. We then discuss how these structures behave under ultra-discretization, a fundamental procedure relating different integrable systems. In particular, we present results showing that the Yang-Baxter and IP properties are preserved under a suitable ultra-discretization, leading to new piecewise-linear examples having these two properties and raising questions about stationary measures of ultra-discrete integrable systems.
Makiko Sasada, University of Tokyo
" Independence Preserving Property in Integrable Systems and Ultra-discretization"
Abstract: The independence preserving (IP) property has long been studied in probability theory, and it has recently been recognized to play an important role in the analysis of stationary distributions of certain integrable systems. In this talk, we first review connections between the IP property and integrable systems, including both classical and stochastic integrable systems. We then discuss how these structures behave under ultra-discretization, a fundamental procedure relating different integrable systems. In particular, we present results showing that the Yang-Baxter and IP properties are preserved under a suitable ultra-discretization, leading to new piecewise-linear examples having these two properties and raising questions about stationary measures of ultra-discrete integrable systems.
Everyone is cordially invited!
B. Kołodziejek, W. Matysiak, K. Szpojankowski, J. Wesołowski