359 citations · 1k across the 39 of their papers we have counts for
41 papers
Homogenization at a polynomial scale in high contrast
Scott Armstrong, Tuomo Kuusi, Amélie Loher
We prove an upper bound on the homogenization length scale which is a fixed power of the coarse ellipticity ratio for coefficient fields that satisfy a finite range of dependence a…
Coarse-grained ellipticity and De Giorgi-Nash-Moser theory
Scott Armstrong, Benny Avelin, Cristiana De Filippis +2
We prove local boundedness and a Harnack inequality for nonnegative weak solutions of the equation under a coarse-grained ellipticity assump…
Superdiffusion and anomalous regularization in self-similar random incompressible flows
Scott Armstrong, Ahmed Bou-Rabee, Tuomo Kuusi
We study the long-time behavior of a particle in , , subject to molecular diffusion and advection by a random incompressible flow. The velocity field is the…
A coarse-graining theory for elliptic operators and homogenization in high contrast
Scott Armstrong, Tuomo Kuusi
We review a coarse-graining theory for divergence-form elliptic operators. The construction centers on a pair of coarse-grained matrices defined on spatial blocks that encode a sca…
Renormalized stochastic pressure equation with log-correlated Gaussian coefficients
Benny Avelin, Tuomo Kuusi, Patrik Nummi +3
We study periodic solutions to the following divergence-form stochastic partial differential equation with Wick-renormalized gradient on the -dimensional flat torus $\mathbb{T}^…
Renormalization group and elliptic homogenization in high contrast
Scott Armstrong, Tuomo Kuusi
We prove a quantitative estimate for the homogenization length scale in terms of the ellipticity ratio of the coefficient field. This upper bound applies to high-contrast ell…