Mixing on Generalized Associahedra
<|reference_start|>Mixing on Generalized Associahedra: Eppstein and Frishberg recently proved that the mixing time for the simple random walk on the $1$-skeleton of the associahedron is $O(n^3\log^3 n)$. 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 $O(n^3\log^3 n)$ in type $B$ and a bound of $O(n^{13} \log^2 n)$ in type $D$; in the process, we establish an expansion bound that is tight up to logarithmic factors in type $B$.<|reference_end|>
@article{chang2024mixing,
    title={Mixing on Generalized Associahedra},
    author={William Chang, Colin Defant, and Daniel Frishberg},
    journal={arXiv preprint arXiv:2408.05611},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.05611},
    primaryClass={math.CO cs.DS math.PR}
}