7 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…
Formalization of De Giorgi--Nash--Moser Theory in Lean
Scott Armstrong, Julia Kempe
We present a formalization in Lean of the core interior De Giorgi--Nash--Moser theory for uniformly elliptic divergence-form equations with bounded measurable coefficients. The for…
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…
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…
Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift
Scott Armstrong, Ahmed Bou-Rabee, Tuomo Kuusi
We consider the long-time behavior of a diffusion process on advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetri…