Randomized box-ball systems, limit shape of rigged configurations and Thermodynamic Bethe ansatz

Atsuo Kuniba, Hanbaek Lyu, Masato Okado

We introduce a probability distribution on the set of states in a generalized box-ball system associated with Kirillov-Reshetikhin (KR) crystals of type $A_n^{(1)}$. Their conserve…