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- W4353079968 abstract "We investigate the large-distance asymptotics of optimal Hardy weights on $mathbb Z^d$, $dgeq 3$, via the super solution construction. For the free discrete Laplacian, the Hardy weight asymptotic is the familiar $frac{(d-2)^2}{4}|x|^{-2}$ as $|x|toinfty$. We prove that the inverse-square behavior of the optimal Hardy weight is robust for general elliptic coefficients on $mathbb Z^d$: (1) averages over large sectors have inverse-square scaling, (2), for ergodic coefficients, there is a pointwise inverse-square upper bound on moments, and (3), for i.i.d. coefficients, there is a matching inverse-square lower bound on moments. The results imply $|x|^{-4}$-scaling for Rellich weights on $mathbb Z^d$. Analogous results are also new in the continuum setting. The proofs leverage Green's function estimates rooted in homogenization theory." @default.
- W4353079968 created "2023-03-23" @default.
- W4353079968 creator A5009817680 @default.
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- W4353079968 date "2021-03-31" @default.
- W4353079968 modified "2023-09-27" @default.
- W4353079968 title "Optimal Hardy weights on the Euclidean lattice" @default.
- W4353079968 doi "https://doi.org/10.48550/arxiv.2103.17019" @default.
- W4353079968 hasPublicationYear "2021" @default.
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