A Markov Chain Arising from the Hopf Square Map on a Non-cocommutative Quantum Group
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912632457396224 |
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| author | Snyder, Donovan |
| author_facet | Snyder, Donovan |
| contents | Expanding upon the rich history of algebraic techniques in probability, we show the existence of and construct a Markov chain using the Hopf square map on a quantum group that is both non-commutative and non-cocommutative. This extends the work of Diaconis, Pang, and Ram to other Hopf algebras. The new, one-dimensional chain requires different analytical approaches. In this case we use standard martingale theory to prove the existence of a phase transition and prove bounds on the expected growth rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05298 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Markov Chain Arising from the Hopf Square Map on a Non-cocommutative Quantum Group Snyder, Donovan Probability 60J10 (Primary), 60G42 (Secondary) Expanding upon the rich history of algebraic techniques in probability, we show the existence of and construct a Markov chain using the Hopf square map on a quantum group that is both non-commutative and non-cocommutative. This extends the work of Diaconis, Pang, and Ram to other Hopf algebras. The new, one-dimensional chain requires different analytical approaches. In this case we use standard martingale theory to prove the existence of a phase transition and prove bounds on the expected growth rates. |
| title | A Markov Chain Arising from the Hopf Square Map on a Non-cocommutative Quantum Group |
| topic | Probability 60J10 (Primary), 60G42 (Secondary) |
| url | https://arxiv.org/abs/2510.05298 |