SL(2,R) Yang-Mills theory on a circle

The kinematics of SL(2,R) Yang-Mills theory on a circle is considered, for reasons that are spelled out. The gauge transformations exhibit hyperbolic fixed points, and this results in a physical configuration space with a non-Hausdorff "network" topology. The ambiguity encountered in canonical quantization is then much more pronounced than in the compact case, and can not be resolved through the kind of appeal made to group theory in that case.Comment: 10 pages, Goteborg ITP 94-19, Contains two files: A latex file with all figures drawn in latex and a tar archive including a slightly modified latex file (uses psfig) and nicer postscript figures+necessary macro

Asymptotic power of sphericity tests for high-dimensional data

This paper studies the asymptotic power of tests of sphericity against perturbations in a single unknown direction as both the dimensionality of the data and the number of observations go to infinity. We establish the convergence, under the null hypothesis and contiguous alternatives, of the log ratio of the joint densities of the sample covariance eigenvalues to a Gaussian process indexed by the norm of the perturbation. When the perturbation norm is larger than the phase transition threshold studied in Baik, Ben Arous and Peche [Ann. Probab. 33 (2005) 1643-1697] the limiting process is degenerate, and discrimination between the null and the alternative is asymptotically certain. When the norm is below the threshold, the limiting process is nondegenerate, and the joint eigenvalue densities under the null and alternative hypotheses are mutually contiguous. Using the asymptotic theory of statistical experiments, we obtain asymptotic power envelopes and derive the asymptotic power for various sphericity tests in the contiguity region. In particular, we show that the asymptotic power of the Tracy-Widom-type tests is trivial (i.e., equals the asymptotic size), whereas that of the eigenvalue-based likelihood ratio test is strictly larger than the size, and close to the power envelope.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1100 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic normality of the Parzen-Rosenblatt density estimator for strongly mixing random fields

We prove the asymptotic normality of the kernel density estimator (introduced by Rosenblatt (1956) and Parzen (1962)) in the context of stationary strongly mixing random fields. Our approach is based on the Lindeberg's method rather than on Bernstein's small-block-large-block technique and coupling arguments widely used in previous works on nonparametric estimation for spatial processes. Our method allows us to consider only minimal conditions on the bandwidth parameter and provides a simple criterion on the (non-uniform) strong mixing coefficients which do not depend on the bandwith.Comment: 16 page

Estimating factor models for multivariate volatilities : an innovation expansion method

We introduce an innovation expansion method for estimation of factor models for conditional variance (volatility) of a multivariate time series. We estimate the factor loading space and the number of factors by a stepwise optimization algorithm on expanding the "white noise space". Simulation and a real data example are given for illustration

Representations of the SU(N)SU(N) TT-algebra and the loop representation in 1+11+1-dimensions

We consider the phase-space of Yang-Mills on a cylindrical space-time ($S^1 \times {\bf R}$) and the associated algebra of gauge-invariant functions, the $T$-variables. We solve the Mandelstam identities both classically and quantum-mechanically by considering the $T$-variables as functions of the eigenvalues of the holonomy and their associated momenta. It is shown that there are two inequivalent representations of the quantum $T$-algebra. Then we compare this reduced phase space approach to Dirac quantization and find it to give essentially equivalent results. We proceed to define a loop representation in each of these two cases. One of these loop representations (for $N=2$) is more or less equivalent to the usual loop representation.Comment: 15 pages, LaTeX, 1 postscript figure included, uses epsf.sty, G\"oteborg ITP 93-3

Optical calibration hardware for the Sudbury Neutrino Observatory

The optical properties of the Sudbury Neutrino Observatory (SNO) heavy water Cherenkov neutrino detector are measured in situ using a light diffusing sphere ("laserball"). This diffuser is connected to a pulsed nitrogen/dye laser via specially developed underwater optical fibre umbilical cables. The umbilical cables are designed to have a small bending radius, and can be easily adapted for a variety of calibration sources in SNO. The laserball is remotely manipulated to many positions in the D2O and H2O volumes, where data at six different wavelengths are acquired. These data are analysed to determine the absorption and scattering of light in the heavy water and light water, and the angular dependence of the response of the detector's photomultiplier tubes. This paper gives details of the physical properties, construction, and optical characteristics of the laserball and its associated hardware.Comment: 17 pages, 8 figures, submitted to Nucl. Inst. Meth.

Magnetic polarizability of hadrons from lattice QCD

We extract the magnetic polarizability from the quadratic response of a hadron's mass shift in progressively small static magnetic fields. The calculation is done on a 24x12x12x24 lattice at a = 0.17 fm with an improved gauge action and the clover quark action. The results are compared to those from experiments and models where available.Comment: 3 pages, 3 figures, contribution to Lattice 2002 (spectrum

What makes for prize-winning television?

We investigate the determinants of success in four international television awards festivals between 1994 and 2012. We find that countries with larger markets and greater expenditure on public broadcasting tend to win more awards, but that the degree of concentration in the market for television and rates of penetration of pay-per-view television are unrelated to success. These findings are consistent with general industrial organisation literature on quality and market size, and with media policy literature on public service broadcasting acting as a force for quality. However, we also find that ‘home countries’ enjoy a strong advantage in these festivals, which is not consistent with festival success acting as a pure proxy for television quality