Sharp character bounds and cutoff for symmetric groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915422727569408 |
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| author | Olesker-Taylor, Sam Teyssier, Lucas Thévenin, Paul |
| author_facet | Olesker-Taylor, Sam Teyssier, Lucas Thévenin, Paul |
| contents | We develop a flexible technique to bound the characters of symmetric groups, via the Naruse hook length formula, the Larsen--Shalev character bounds, and appropriate diagram slicings. It allows us to prove a uniform exponential character bound with optimal constant $1/2$. We furthermore prove sharp character bounds for conjugacy classes having a macroscopic number of fixed points, and deduce that the random walks on the associated Cayley graphs exhibit a total variation and $L^2$ cutoff. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp character bounds and cutoff for symmetric groups Olesker-Taylor, Sam Teyssier, Lucas Thévenin, Paul Representation Theory Combinatorics Group Theory Probability 20C30 (Primary) 60J10, 05E10 (Secondary) We develop a flexible technique to bound the characters of symmetric groups, via the Naruse hook length formula, the Larsen--Shalev character bounds, and appropriate diagram slicings. It allows us to prove a uniform exponential character bound with optimal constant $1/2$. We furthermore prove sharp character bounds for conjugacy classes having a macroscopic number of fixed points, and deduce that the random walks on the associated Cayley graphs exhibit a total variation and $L^2$ cutoff. |
| title | Sharp character bounds and cutoff for symmetric groups |
| topic | Representation Theory Combinatorics Group Theory Probability 20C30 (Primary) 60J10, 05E10 (Secondary) |
| url | https://arxiv.org/abs/2503.12735 |