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pro vyhledávání: '"Armstrong, Scott A."'
Autor:
Armstrong, Scott, Kuusi, Tuomo
We prove a quantitative estimate on the homogenization length scale in terms of the ellipticity ratio~$\Lambda/\lambda$ of the coefficient field. This upper bound applies to high-contrast elliptic equations demonstrating near-critical behavior. Speci
Externí odkaz:
http://arxiv.org/abs/2405.10732
We consider the long-time behavior of a diffusion process on $\mathbb{R}^d$ advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetric in law and have a log-correlated potential. A special case includes
Externí odkaz:
http://arxiv.org/abs/2404.01115
We prove optimal convergence rates for eigenvalues and eigenvectors of the graph Laplacian on Poisson point clouds. Our results are valid down to the critical percolation threshold, yielding error estimates for relatively sparse graphs.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/2312.08149
Autor:
Armstrong, Scott, Wu, Wei
We prove that the scaling limit of the continuous solid-on-solid model in $\mathbb{Z}^d$ is a multiple of the Gaussian free field.
Comment: 40 pages
Comment: 40 pages
Externí odkaz:
http://arxiv.org/abs/2310.13630
We prove quantitative homogenization results for harmonic functions on supercritical continuum percolation clusters--that is, Poisson point clouds with edges connecting points which are closer than some fixed distance. We show that, on large scales,
Externí odkaz:
http://arxiv.org/abs/2309.12900
Autor:
Armstrong, Scott, Vicol, Vlad
For every $\alpha < \frac13$, we construct an explicit divergence-free vector field $\mathbf{b}(t,x)$ which is periodic in space and time and belongs to $C^0_t C^{\alpha}_x \cap C^{\alpha}_t C^0_x$ such that the corresponding scalar advection-diffusi
Externí odkaz:
http://arxiv.org/abs/2305.05048
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 nondivergence form. We consequently obtain a quenched, local CLT for the corr
Externí odkaz:
http://arxiv.org/abs/2211.13279
Autor:
Armstrong, Scott, Kuusi, Tuomo
We give a self-contained introduction to the theory of elliptic homogenization for random coefficient fields, starting from classical qualitative homogenization. The presentation also contains new results, such as optimal estimates (both in terms of
Externí odkaz:
http://arxiv.org/abs/2210.06488
We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schr\"{o}dinger-type operator with a confining potential and with principle part a periodic elliptic operator in divergence form. We compare the spectrum to the homogenized op
Externí odkaz:
http://arxiv.org/abs/2209.12220
Autor:
Heikamp, Emily B., Martucci, Cynthia, Henrich, Jill A., Neel, Dana S., Mahendra-Rajah, Sanisha, Rice, Hannah, Wenge, Daniela V., Perner, Florian, Wen, Yanhe, Hatton, Charlie, Armstrong, Scott A.
Publikováno v:
In Cell Reports 26 November 2024 43(11)
