Asymptotic Renyi Entropies of Random Walks on Groups
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910476997230592 |
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| author | Golubeva, Kimberly Pan, Minghao Tamuz, Omer |
| author_facet | Golubeva, Kimberly Pan, Minghao Tamuz, Omer |
| contents | We introduce asymptotic Rényi entropies as a parameterized family of invariants for random walks on groups. These invariants interpolate between various well-studied properties of the random walk, including the growth rate of the group, the Shannon entropy, and the spectral radius. They furthermore offer large deviation counterparts of the Shannon-McMillan-Breiman Theorem. We prove some basic properties of asymptotic Rényi entropies that apply to all groups, and discuss their analyticity and positivity for the free group and lamplighter groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_15827 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic Renyi Entropies of Random Walks on Groups Golubeva, Kimberly Pan, Minghao Tamuz, Omer Probability Group Theory We introduce asymptotic Rényi entropies as a parameterized family of invariants for random walks on groups. These invariants interpolate between various well-studied properties of the random walk, including the growth rate of the group, the Shannon entropy, and the spectral radius. They furthermore offer large deviation counterparts of the Shannon-McMillan-Breiman Theorem. We prove some basic properties of asymptotic Rényi entropies that apply to all groups, and discuss their analyticity and positivity for the free group and lamplighter groups. |
| title | Asymptotic Renyi Entropies of Random Walks on Groups |
| topic | Probability Group Theory |
| url | https://arxiv.org/abs/2307.15827 |