Cutoff Phenomenon for Cyclic Dynamics on Hypercube
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866910491431927808 |
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| author | Lim, Keunwoo |
| author_facet | Lim, Keunwoo |
| contents | The cutoff phenomena for Markovian dynamics have been observed and rigorously verified for a multitude of models, particularly for Glauber-type dynamics on spin systems. However, prior studies have barely considered irreversible chains. In this work, the cutoff phenomenon of certain cyclic dynamics are studied on the hypercube $Σ_{n} = Q^{V_{n}}$, where $Q = \{1, 2, 3\}$ and $V_{n} = \{1,...,n\}$. The main feature of these dynamics is the fact that they are represented by an irreversible Markov chain. Based on the coupling modifications suggested in a previous study of the cutoff phenomenon for the Curie-Weiss-Potts model, a comprehensive proof is presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_01756 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Cutoff Phenomenon for Cyclic Dynamics on Hypercube Lim, Keunwoo Probability The cutoff phenomena for Markovian dynamics have been observed and rigorously verified for a multitude of models, particularly for Glauber-type dynamics on spin systems. However, prior studies have barely considered irreversible chains. In this work, the cutoff phenomenon of certain cyclic dynamics are studied on the hypercube $Σ_{n} = Q^{V_{n}}$, where $Q = \{1, 2, 3\}$ and $V_{n} = \{1,...,n\}$. The main feature of these dynamics is the fact that they are represented by an irreversible Markov chain. Based on the coupling modifications suggested in a previous study of the cutoff phenomenon for the Curie-Weiss-Potts model, a comprehensive proof is presented. |
| title | Cutoff Phenomenon for Cyclic Dynamics on Hypercube |
| topic | Probability |
| url | https://arxiv.org/abs/2010.01756 |