Eppstein and Frishberg recently proved that the mixing time for the simple random walk on the $1$-skeleton of the associahedron is O(n³log³ n). We obtain similar rapid mixing results for the simple random walks on the $1$-skeleta of the type-B and type-D associahedra. We adapt Eppstein and Frishberg's technique to obtain the same bound of O(n³log³ n) in type B and a bound of O(n¹³ log² n) in type D; in the process, we establish an expansion bound that is tight up to logarithmic factors in type B.
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Chang et al. (2024) studied this question.
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