# Homogenization of iterated singular integrals with applications to random quasiconformal maps.

@article{Astala2020HomogenizationOI, title={Homogenization of iterated singular integrals with applications to random quasiconformal maps.}, author={Kari Astala and Steffen Rohde and Eero Saksman and Terence Tao}, journal={arXiv: Complex Variables}, year={2020} }

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 $|\mu_j|\leq k<1$ and has locally periodic statistics, for example of the type $$\mu_j (z,\omega)=\phi(z…

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