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- W2950651918 abstract "We construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle. The homeomorphism is constructed using the exponential of $beta X$ where $X$ is the restriction of the two dimensional free field on the circle and the parameter $beta$ is in the high temperature regime $beta<sqrt 2$. The welding problem is solved by studying a non-uniformly elliptic Beltrami equation with a random complex dilatation. For the existence a method of Lehto is used. This requires sharp probabilistic estimates to control conformal moduli of annuli and they are proven by decomposing the free field as a sum of independent fixed scale fields and controlling the correlations of the complex dilation restricted to dyadic cells of various scales. For uniqueness we invoke a result by Jones and Smirnov on conformal removability of Holder curves. We conjecture that our curves are locally related to SLE$(kappa)$ for $kappa<4$." @default.
- W2950651918 created "2019-06-27" @default.
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- W2950651918 date "2009-09-07" @default.
- W2950651918 modified "2023-09-27" @default.
- W2950651918 title "Random Conformal Weldings" @default.
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