All quadrirational Yang-Baxter maps in a key subclass on positive reals have the independence preserving property and generate most known IP bijections via specialization or limits.
Kołodziejek, The matsumoto–yor property and its converse on symmetric co nes, Journal of Theoretical Prob- ability 30 (2017), no
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Yang-Baxter maps and independence preserving property
All quadrirational Yang-Baxter maps in a key subclass on positive reals have the independence preserving property and generate most known IP bijections via specialization or limits.