• Corpus ID: 219966731

# 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}
}
• Published 20 June 2020
• Mathematics
• arXiv: Complex Variables
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…

## References

SHOWING 1-10 OF 26 REFERENCES

### An optimal variance estimate in stochastic homogenization of discrete elliptic equations

• Mathematics
• 2011
We consider a discrete elliptic equation with random coefficients $A$, which (to fix ideas) are identically distributed and independent from grid point to grid point $x\in\mathbb{Z}^d$. On scales

### Liouville quantum gravity and KPZ

• Mathematics
• 2008
AbstractConsider a bounded planar domain D, an instance h of the Gaussian free field on D, with Dirichlet energy (2π)−1∫D∇h(z)⋅∇h(z)dz, and a constant 0≤γ<2. The Liouville quantum gravity measure on

### Regularity and stochastic homogenization of fully nonlinear equations without uniform ellipticity

• Mathematics
• 2014
We prove regularity and stochastic homogenization results for certain degenerate elliptic equations in nondivergence form. The equation is required to be strictly elliptic, but the ellipticity may

### Random conformal weldings

• Mathematics
• 2009
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 βX,

### On mappings with integrable dilatation

• Mathematics
• 1993
A factorization of Stoilow's type has been obtained for mappings in R2 with integrable dilatation. 0. INTRODUCTION For Q a domain in Rn (an open and connected set), we consider a mapping -f Rn of the

### Scaling limits of loop-erased random walks and uniform spanning trees

AbstractThe uniform spanning tree (UST) and the loop-erased random walk (LERW) are strongly related probabilistic processes. We consider the limits of these models on a fine grid in the plane, as the

### Conformally Invariant Processes in the Plane

Theoretical physicists have predicted that the scaling limits of many two-dimensional lattice models in statistical physics are in some sense conformally invariant. This belief has allowed physicists

### Dimer Models and Conformal Structures.

• Mathematics
• 2020
Dimer models have been the focus of intense research efforts over the last years. This paper grew out of an effort to develop new methods to study minimizers or the asymptotic height functions of

### Quantitative Stochastic Homogenization and Large-Scale Regularity

• Mathematics
Grundlehren der mathematischen Wissenschaften
• 2019
This is a preliminary version of a book which presents the quantitative homogenization and large-scale regularity theory for elliptic equations in divergence-form. The self-contained presentation