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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2205.14238 |
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| _version_ | 1866929642780229632 |
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| author | Amir, Gideon Yang, Shangjie |
| author_facet | Amir, Gideon Yang, Shangjie |
| contents | We introduce an "intermediate branching number"(IBN) which captures the branching of intermediate growth trees, similar in spirit to the well-studied branching number of exponential growth trees. We show that the IBN is the critical threshold for several random processes on trees, and analyze the IBN on some examples of interest. Our main result is an algorithm to find spherically symmetric trees with large IBN inside some permutation wreath products. We demonstrate the usefulness of these trees to the study of intermediate growth groups by using them to get the first tight bounds for the firefighter problem on some inetrmediate growth groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_14238 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The branching number of intermediate growth trees Amir, Gideon Yang, Shangjie Probability Group Theory 60K35, 60K37, 20E08 We introduce an "intermediate branching number"(IBN) which captures the branching of intermediate growth trees, similar in spirit to the well-studied branching number of exponential growth trees. We show that the IBN is the critical threshold for several random processes on trees, and analyze the IBN on some examples of interest. Our main result is an algorithm to find spherically symmetric trees with large IBN inside some permutation wreath products. We demonstrate the usefulness of these trees to the study of intermediate growth groups by using them to get the first tight bounds for the firefighter problem on some inetrmediate growth groups. |
| title | The branching number of intermediate growth trees |
| topic | Probability Group Theory 60K35, 60K37, 20E08 |
| url | https://arxiv.org/abs/2205.14238 |