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Some generalization of Pitman’s transform and invariant measures for discrete integrable systems

Presented by: 
Makiko Sasada University of Tokyo
Date: 
Friday 14th December 2018 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
In this talk, I will introduce some generalization of Pitman’s transform and show that the dynamics of several discrete integrable systems, such as the discrete Korteweg-de Vries equation, the ultra-discrete Korteweg-de Vries equation, the ultra-discrete Toda equation, the box-ball system, are given by them. We apply this observation to define infinite space versions of these models and study their invariant measures using the generalized Pitman’s transform. This talk is based on a joint work with David Croydon, Tsuyoshi Kato and Satoshi Tsujimoto.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons