We prove that the well-studied triangulation flip walk on a convex point set mixes in time $O(n^{4.75}),$ the first progress since McShine and Tetali's $O(n^5 \log n)$ bound in 1997. In the process we determine the expansion of the associahedron graph $K_n$ up to a factor of $O(n^{3/4})$. To obtain these results, we extend a framework we developed in a previous preprint--extending the projection-restriction technique of Jerrum, Son, Tetali, and Vigoda--for establishing conditions under which the Glauber dynamics on independent sets and other combinatorial structures mix rapidly.

翻译：我们证明,研究周密的三角曲线在连接点上行走,在时间(O(n ⁇ 4.75})上设定了混合,这是自1997年McShine和Tetali的美元(n ⁇ 5\log n)于1997年受约束以来的第一个进展。在这个过程中,我们决定扩大“组合图”以K美元计,以至10美元计。为了取得这些结果,我们扩展了我们以前在预先打印和延长Jerrum、Son、Tetali和Vigoda的投影-限制技术中开发的一个框架,以建立独立机组和其他组合结构的Grauber动态快速混合的条件。