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Perspectives for Spintronics in 2D Materials
The past decade has been especially creative for spintronics since the
(re)discovery of various two dimensional (2D) materials. Due to the unusual
physical characteristics, 2D materials have provided new platforms to probe the
spin interaction with other degrees of freedom for electrons, as well as to be
used for novel spintronics applications. This review briefly presents the most
important recent and ongoing research for spintronics in 2D materials.Comment: 16 pages, 6 figure
Covariance matrix estimation for stationary time series
We obtain a sharp convergence rate for banded covariance matrix estimates of
stationary processes. A precise order of magnitude is derived for spectral
radius of sample covariance matrices. We also consider a thresholded covariance
matrix estimator that can better characterize sparsity if the true covariance
matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911)
351-376] idea and relate eigenvalues of covariance matrices to the spectral
densities or Fourier transforms of the covariances. We develop a large
deviation result for quadratic forms of stationary processes using m-dependence
approximation, under the framework of causal representation and physical
dependence measures.Comment: Published in at http://dx.doi.org/10.1214/11-AOS967 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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