Regularity of the SLE$_4$ uniformizing map and the SLE$_8$ trace
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909028522655744 |
|---|---|
| author | Kavvadias, Konstantinos Miller, Jason Schoug, Lukas |
| author_facet | Kavvadias, Konstantinos Miller, Jason Schoug, Lukas |
| contents | We show that the modulus of continuity of the SLE$_4$ uniformizing map is given by $(\log δ^{-1})^{-1/3+o(1)}$ as $δ\to 0$. As a consequence of our analysis, we show that the Jones-Smirnov condition for conformal removability (with quasihyperbolic geodesics) does not hold for SLE$_4$. We also show that the modulus of continuity for SLE$_8$ with the capacity time parameterization is given by $(\log δ^{-1})^{-1/4+o(1)}$ as $δ\to 0$, proving a conjecture of Alvisio and Lawler. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_03365 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Regularity of the SLE$_4$ uniformizing map and the SLE$_8$ trace Kavvadias, Konstantinos Miller, Jason Schoug, Lukas Probability Mathematical Physics Complex Variables We show that the modulus of continuity of the SLE$_4$ uniformizing map is given by $(\log δ^{-1})^{-1/3+o(1)}$ as $δ\to 0$. As a consequence of our analysis, we show that the Jones-Smirnov condition for conformal removability (with quasihyperbolic geodesics) does not hold for SLE$_4$. We also show that the modulus of continuity for SLE$_8$ with the capacity time parameterization is given by $(\log δ^{-1})^{-1/4+o(1)}$ as $δ\to 0$, proving a conjecture of Alvisio and Lawler. |
| title | Regularity of the SLE$_4$ uniformizing map and the SLE$_8$ trace |
| topic | Probability Mathematical Physics Complex Variables |
| url | https://arxiv.org/abs/2107.03365 |