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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.22731 |
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| _version_ | 1866914058723131392 |
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| author | Gournay, Antoine |
| author_facet | Gournay, Antoine |
| contents | In this paper we show that groups for which the probability of return of a random walk is bounded below by $K_1 exp(-K_2n^c)$ have no non-constant harmonic functions with gradient in $\ell^p$. The proof relies on results from $\ell^p$-cohomology, a form of radial isoperimetry, transport patterns and revisiting some results of Følner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22731 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Radial isoperimetry and absence of harmonic functions with $\ell^p$-gradient Gournay, Antoine Group Theory 31C05, 60G50, 20J06, 43A07, 05C81, 20F6 In this paper we show that groups for which the probability of return of a random walk is bounded below by $K_1 exp(-K_2n^c)$ have no non-constant harmonic functions with gradient in $\ell^p$. The proof relies on results from $\ell^p$-cohomology, a form of radial isoperimetry, transport patterns and revisiting some results of Følner. |
| title | Radial isoperimetry and absence of harmonic functions with $\ell^p$-gradient |
| topic | Group Theory 31C05, 60G50, 20J06, 43A07, 05C81, 20F6 |
| url | https://arxiv.org/abs/2509.22731 |