Markov chains, CAT(0) cube complexes, and enumeration: monotone paths in a strip mix slowly
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913500099510272 |
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| author | Ardila-Mantilla, Federico Banerjee, Naya Weir, Coleson |
| author_facet | Ardila-Mantilla, Federico Banerjee, Naya Weir, Coleson |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09133 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Markov chains, CAT(0) cube complexes, and enumeration: monotone paths in a strip mix slowly Ardila-Mantilla, Federico Banerjee, Naya Weir, Coleson Combinatorics Probability 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. |
| title | Markov chains, CAT(0) cube complexes, and enumeration: monotone paths in a strip mix slowly |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2409.09133 |