Frostman dimension of Furstenberg measure for $\mathrm{SL}(2,\mathbb{R})$ random matrix products
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | |
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| _version_ | 1866908776477491200 |
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| author | Rush, Tom |
| author_facet | Rush, Tom |
| contents | For compactly supported $μ\in \mathcal{P}(\mathrm{SL}(2,\mathbb{R}))$ satisfying strong irreducibility and proximality, we obtain a formula for the Frostman dimension of the associated Furstenberg measure. We also describe the left neighbourhood of 0 for which the classical transfer operators defined by Le Page have a spectral gap on Hölder spaces in this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14061 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Frostman dimension of Furstenberg measure for $\mathrm{SL}(2,\mathbb{R})$ random matrix products Rush, Tom Dynamical Systems Probability 28A80, 37C30, 60F10 For compactly supported $μ\in \mathcal{P}(\mathrm{SL}(2,\mathbb{R}))$ satisfying strong irreducibility and proximality, we obtain a formula for the Frostman dimension of the associated Furstenberg measure. We also describe the left neighbourhood of 0 for which the classical transfer operators defined by Le Page have a spectral gap on Hölder spaces in this setting. |
| title | Frostman dimension of Furstenberg measure for $\mathrm{SL}(2,\mathbb{R})$ random matrix products |
| topic | Dynamical Systems Probability 28A80, 37C30, 60F10 |
| url | https://arxiv.org/abs/2601.14061 |