Can I read Markov chains, CAT(0) cube complexes, and enumeration: monotone paths in a strip mix slowly on EtoBox?

Markov chains, CAT(0) cube complexes, and enumeration: monotone paths in a strip mix slowly by Ardila-Mantilla, Federico; Banerjee, Naya; Weir, Coleson is a scholarly article available to read on EtoBox.

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

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 complexes to detect small bottlenecks in many graphs of combinatorial interest. Along the way, we give a formula for the number c_m(n) of monotone paths of length n in a strip of height m. In particular we compute the exponential growth constant of c_m(n) for arbitrary m, generalizing results of Williams for m=2, 3.

Author

Ardila-Mantilla, Federico; Banerjee, Naya; Weir, Coleson

Published

2024

Language

EN