Polynomial mixing for polygonal side matchings
arXiv:2607.02410
Abstract
We introduce a natural Markov chain on chord diagrams, which, at every step, selects two random chords and swaps them if doing so preserves the diagram's genus. This generalizes the chord swap chain on the Catalan structure of non-intersecting chord diagrams. We show that for fixed genus, the chain mixes in polynomial time.
23 pages, 19 figures. Comments welcome!