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

Document detail

ID

oai:arXiv.org:2409.07892

Topic

Mathematics - Probability Computer Science - Computational G... Computer Science - Discrete Mathem... Mathematics - Combinatorics

Author

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

Year

2024

listing date

2/26/2025

Keywords

mathematics

Metrics

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).

;Comment: 20 pages, 6 figures

Anand, Konrad,Feng, Weiming,Freifeld, Graham,Guo, Heng,Jerrum, Mark,Wang, Jiaheng, 2024, Rapid mixing of the flip chain over non-crossing spanning trees