Conformal welding of independent Gaussian multiplicative chaos measures
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918302657282048 |
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| author | Kupiainen, Antti McAuley, Michael Saksman, Eero |
| author_facet | Kupiainen, Antti McAuley, Michael Saksman, Eero |
| contents | We solve the classical conformal welding problem for a composition of two random homeomorphisms generated by independent Gaussian multiplicative chaos measures with small parameter values. In other words, given two such measures on the boundary of the unit disk we show that there exist conformal maps to complementary domains on the Riemann sphere such that the pushforward of the normalised measures agree on their common boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_18062 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conformal welding of independent Gaussian multiplicative chaos measures Kupiainen, Antti McAuley, Michael Saksman, Eero Probability Mathematical Physics Complex Variables 60G57, 30C62, 60J67 We solve the classical conformal welding problem for a composition of two random homeomorphisms generated by independent Gaussian multiplicative chaos measures with small parameter values. In other words, given two such measures on the boundary of the unit disk we show that there exist conformal maps to complementary domains on the Riemann sphere such that the pushforward of the normalised measures agree on their common boundary. |
| title | Conformal welding of independent Gaussian multiplicative chaos measures |
| topic | Probability Mathematical Physics Complex Variables 60G57, 30C62, 60J67 |
| url | https://arxiv.org/abs/2305.18062 |