Zobrazeno 1 - 10
of 75
pro vyhledávání: '"Smart, Charles K"'
Autor:
Chen, Nixia, Smart, Charles K
We show the eigenvectors of a Gaussian random band matrix are localized when the band width is less than the 1/4 power of the matrix size. Our argument is essentially an optimized version of Schenker's proof of the 1/8 exponent.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2206.06439
Autor:
Ding, Jian, Smart, Charles K
We consider a Hamiltonian given by the Laplacian plus a Bernoulli potential on the two dimensional lattice. We prove that, for energies sufficiently close to the edge of the spectrum, the resolvent on a large square is likely to decay exponentially.
Externí odkaz:
http://arxiv.org/abs/1809.09041
Autor:
Calder, Jeff, Smart, Charles K
Publikováno v:
Duke Math. J. 169, no. 11 (2020), 2079-2124
We prove that the convex peeling of a random point set in dimension d approximates motion by the 1/(d + 1) power of Gaussian curvature. We use viscosity solution theory to interpret the limiting partial differential equation. We use the Martingale me
Externí odkaz:
http://arxiv.org/abs/1805.08278
Autor:
Feldman, William M, Smart, Charles K
We study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous Hamiltonian. We find an explicit formula for the Hamiltonian, prove the solutions are unique, and prove that the limiting fre
Externí odkaz:
http://arxiv.org/abs/1711.00965
Autor:
Pegden, Wesley, Smart, Charles K
We show that the patterns in the Abelian sandpile are stable. The proof combines the structure theory for the patterns with the regularity machinery for non-divergence form elliptic equations. The stability results allows one to improve weak-* conver
Externí odkaz:
http://arxiv.org/abs/1708.09432
Publikováno v:
Annales de l'Institut Henri Poincare / Analyse non lineaire. 35, No. 4 (2018), 921--943
We prove a result related to Bressan's mixing problem. We establish an inequality for the change of Bianchini semi-norms of characteristic functions under the flow generated by a divergence free time dependent vector field. The approach leads to a bi
Externí odkaz:
http://arxiv.org/abs/1612.03431
Publikováno v:
Memoirs of the American Mathematical Society, vol. 257, No. 1231 (2019)
We prove $L^{p_1}(\mathbb R^d)\times \dots \times L^{p_{n+2}}(\mathbb R^{d})$ polynomial growth estimates for the Christ-Journ\'e multilinear singular integral forms and suitable generalizations.
Comment: To appear in Memoirs of the AMS
Comment: To appear in Memoirs of the AMS
Externí odkaz:
http://arxiv.org/abs/1510.06990
Autor:
Lin, Jessica, Smart, Charles K.
Publikováno v:
Anal. PDE 8 (2015) 1497-1539
This article establishes an algebraic error estimate for the stochastic homogenization of fully nonlinear uniformly parabolic equations in stationary ergodic spatio-temporal media. The approach is similar to that of Armstrong and Smart in the study o
Externí odkaz:
http://arxiv.org/abs/1501.03718
Autor:
Armstrong, Scott N., Smart, Charles K.
We present quantitative results for the homogenization of uniformly convex integral functionals with random coefficients under independence assumptions. The main result is an error estimate for the Dirichlet problem which is algebraic (but sub-optima
Externí odkaz:
http://arxiv.org/abs/1406.0996
Consider a discrete-time martingale $\{X_t\}$ taking values in a Hilbert space $\mathcal H$. We show that if for some $L \geq 1$, the bounds $\mathbb{E} \left[\|X_{t+1}-X_t\|_{\mathcal H}^2 \mid X_t\right]=1$ and $\|X_{t+1}-X_t\|_{\mathcal H} \leq L$
Externí odkaz:
http://arxiv.org/abs/1405.5980