1. Homogenization of iterated singular integrals with applications to random quasiconformal maps
- Author
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Astala, Kari, Rohde, Steffen, Saksman, Eero, Tao, Terence, Department of Mathematics and Statistics, Kari Astala / Principal Investigator, and Geometric Analysis and Partial Differential Equations
- Subjects
Homogenization ,Mathematics - Complex Variables ,General Mathematics ,Probability (math.PR) ,Singular integrals ,FOS: Mathematics ,111 Mathematics ,Complex Variables (math.CV) ,random Beltrami coefficients ,Mathematics - Probability ,Quasiconformal maps - Abstract
We study homogenization of iterated randomized singular integrals and homeomorphic solutions to the Beltrami differential equation with a random Beltrami coefficient. More precisely, let $(F_j)_{j \geq 1}$ be a sequence of normalized homeomorphic solutions to the planar Beltrami equation $\overline{\partial} F_j (z)=\mu_j(z,\omega) \partial F_j(z),$ where the random dilatation satisfies $|\mu_j|\leq k, Comment: 56 pages
- Published
- 2022
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