Markov chains, CAT(0) cube complexes, and enumeration: monotone paths in a strip mix slowly

Federico Ardila-Mantilla, Naya Banerjee, Coleson Weir

We prove that two natural Markov chains on the set of monotone paths in a strip mix slowly. To do so, we make novel use of the theory of non-positively curved (CAT(0)) cubical comp…