Beyond universality in random matrix theory

In order to have a better understanding of finite random matrices with non-Gaussian entries, we study the $1/N$ expansion of local eigenvalue statistics in both the bulk and at the hard edge of the spectrum of random matrices. This gives valuable information about the smallest singular value not seen in universality laws. In particular, we show the dependence on the fourth moment (or the kurtosis) of the entries. This work makes use of the so-called complex Gaussian divisible ensembles for both Wigner and sample covariance matrices.Comment: Published at http://dx.doi.org/10.1214/15-AAP1129 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Density of States of Quantum Spin Systems from Isotropic Entanglement

We propose a method which we call "Isotropic Entanglement" (IE), that predicts the eigenvalue distribution of quantum many body (spin) systems (QMBS) with generic interactions. We interpolate between two known approximations by matching fourth moments. Though, such problems can be QMA-complete, our examples show that IE provides an accurate picture of the spectra well beyond what one expects from the first four moments alone. We further show that the interpolation is universal, i.e., independent of the choice of local terms.Comment: 4+ pages, content is as in the published versio

The Oil Pollution Act of 1990

In response to several major oil spills, including the Exxon Valdez incident in 1989, the Oil Pollution Act of 1990 (OPA) was signed into law. The author reviews responses to various oil spills, and the inadequacy of legislation applicable to such responses prior to the OPA. This article reviews various sections of the OPA and the breadth of its coverage. The author points out that this new legislation expands liability with respect to oil spills, providing an incentive to potentially responsible tanker owners to take stronger measures to avoid such spills. However, as the author explains, the OPA may create as many problems as it solves. For example, insurers may have to provide new insurance coverage due to larger exposure under the OPA, or even stop providing such insurance altogether. The OPA requires that barges be double hulled, which is extremely costly to install and may be the cause of more explosions or extensive leaks than single hulls. The author also opines that the increased liability under the OPA may deter foreign oil importers from using the ports of the United States

Preliminary results of noble metal thermocouple research program, 1000 - 2000 C

Noble metal thermocouple research involving combustion gase

Eigenvalue distributions of beta-Wishart matrices

We derive explicit expressions for the distributions of the extreme eigenvalues of the Beta-Wishart random matrices in terms of the hypergeometric function of a matrix argument. These results generalize the classical results for the real (β = 1), complex (β = 2), and quaternion (β = 4) Wishart matrices to any β > 0