186 citations · 1k across the 57 of their papers we have counts for
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Anomalous diffusion by fractal homogenization
Scott Armstrong, Vlad Vicol
For every , we construct an explicit divergence-free vector field which is periodic in space and time and belongs to su…
Green function and invariant measure estimates for nondivergence form elliptic homogenization
Scott Armstrong, Benjamin Fehrman, Jessica Lin
We prove quantitative estimates on the the parabolic Green function and the stationary invariant measure in the context of stochasic homogenization of elliptic equations in nondive…
Elliptic homogenization from qualitative to quantitative
Scott Armstrong, Tuomo Kuusi
We give a self-contained introduction to the theory of elliptic homogenization for random coefficient fields, starting from classical qualitative homogenization. The presentation a…
Asymptotic expansion of the spectrum for periodic Schrödinger operators
Scott Armstrong, Raghavendra Venkatraman
We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schrödinger-type operator with a confining potential and with principle part a periodic elliptic operator…
Optimal unique continuation for periodic elliptic equations on large scales
Scott Armstrong, Tuomo Kuusi, Charles Smart
We prove a quantitative, large-scale doubling inequality and large-scale three-ellipsoid inequality for solutions of uniformly elliptic equations with periodic coefficients. These…
Large-scale analyticity and unique continuation for periodic elliptic equations
Scott Armstrong, Tuomo Kuusi, Charles Smart
We prove that a solution of an elliptic operator with periodic coefficients behaves on large scales like an analytic function, in the sense of approximation by polynomials with per…