We show that the flip chain for non-crossing spanning trees of n+1 points in convex position mixes in time O(n⁸log 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).
@InProceedings{anand_et_al:LIPIcs.SoCG.2025.8, author = {Anand, Konrad and Feng, Weiming and Freifeld, Graham and Guo, Heng and Jerrum, Mark and Wang, Jiaheng}, title = {{Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees}}, booktitle = {41st International Symposium on Computational Geometry (SoCG 2025)}, pages = {8:1--8:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-370-6}, ISSN = {1868-8969}, year = {2025}, volume = {332}, editor = {Aichholzer, Oswin and Wang, Haitao}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.8}, URN = {urn:nbn:de:0030-drops-231607}, doi = {10.4230/LIPIcs.SoCG.2025.8}, annote = {Keywords: non-crossing spanning trees, Markov chain, mixing time} }
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