Tuomo Kuusi and I have formalized some of the main results of our recent paper on quantitative stochastic homogenization in the Lean 4 proof assistant. The repository is available here. In that paper we developed a coarse-graining theory for elliptic equations in divergence form, which was applied to obtain quantitative stochastic homogenization results in the […]
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Julia Kempe and I have just completed a Lean 4 formalization of De Giorgi–Nash–Moser theory. We formalized the full slate of interior regularity statements for weak solutions of divergence-form elliptic equations with merely bounded measurable (and not necessarily symmetric) coefficients, including local boundedness, the weak Harnack and Harnack inequalities, and finally interior Hölder regularity. The
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Tuomo Kuusi and I have just posted our paper “Renormalization group and elliptic homogenization in high contrast” to the arXiv. The paper is about quantitative homogenization of the elliptic equation (1) where is a matrix-valued coefficient field. In our setup, we assume that satisfies a suitable ellipticity condition (more on that below) and that
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We have just uploaded our paper, joint with Ahmed Bou-Rabee and Tuomo Kuusi, titled “Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift,” to the arXiv. The results in this paper were recently announced by Ahmed in several public talks, including this one at the Fields Institute. The paper is
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Vlad Vicol and I have just uploaded our paper “Anomalous diffusion by fractal homogenization” to the arxiv. It contains results previously announced last June at the “Probability and Mathematical Physics” conference in Helsinki and in subsequent seminar talks by both of us since then. (A recording of my Helsinki talk can be found here.) In
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Tuomo Kuusi and I have written a new book-length manuscript with the title “Elliptic Homogenization from Qualitative to Quantitative” which we have just posted to the arxiv. This is intended as an introductory text for graduate students and researchers interested in quantitative homogenization for elliptic equations in divergence form. We assume no previous knowledge of
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