Rapid mixing of the flip chain over non-crossing spanning trees

Konrad Anand; Weiming Feng; Graham Freifeld; Heng Guo; Mark Jerrum; Jiaheng Wang

Rapid mixing of the flip chain over non-crossing spanning trees

Probability 2025-02-20 v2 Computational Geometry Discrete Mathematics Combinatorics

Authors: Konrad Anand , Weiming Feng , Graham Freifeld , Heng Guo , Mark Jerrum , Jiaheng Wang

Abstract

We show that the flip chain for non-crossing spanning trees of $n+1$ points in convex position mixes in time $O(n^8\log n)$ . We use connections between Fuss-Catalan structures to construct a comparison argument with a chain similar to Wilson's lattice path chain (Wilson 2004).

Keywords

flip chain non-crossing spanning trees rapid mixing Markov chain Monte Carlo Fuss-Catalan structures comparison argument

Cite

@article{arxiv.2409.07892,
  title  = {Rapid mixing of the flip chain over non-crossing spanning trees},
  author = {Konrad Anand and Weiming Feng and Graham Freifeld and Heng Guo and Mark Jerrum and Jiaheng Wang},
  journal= {arXiv preprint arXiv:2409.07892},
  year   = {2025}
}

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20 pages, 6 figures

Rapid mixing of the flip chain over non-crossing spanning trees

Abstract

Keywords

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