Asymptotic properties of eigenmatrices of a large sample covariance matrix

Let $S_n=\frac{1}{n}X_nX_n^*$ where $X_n=\{X_{ij}\}$ is a $p\times n$ matrix with i.i.d. complex standardized entries having finite fourth moments. Let $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)=\sqrt{p}({\mathbf {x}}_n(\mathbf {t}_1)^*(S_n+\sigma I)^{-1}{\mathbf {x}}_n(\mathbf {t}_2)-{\mathbf {x}}_n(\mathbf {t}_1)^*{\mathbf {x}}_n(\mathbf {t}_2)m_n(\sigma))$ in which $\sigma>0$ and $m_n(\sigma)=\int\frac{dF_{y_n}(x)}{x+\sigma}$ where $F_{y_n}(x)$ is the Mar\v{c}enko--Pastur law with parameter $y_n=p/n$; which converges to a positive constant as $n\to\infty$, and ${\mathbf {x}}_n(\mathbf {t}_1)$ and ${\mathbf {x}}_n(\mathbf {t}_2)$ are unit vectors in ${\Bbb{C}}^p$, having indices $\mathbf {t}_1$ and $\mathbf {t}_2$, ranging in a compact subset of a finite-dimensional Euclidean space. In this paper, we prove that the sequence $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)$ converges weakly to a $(2m+1)$-dimensional Gaussian process. This result provides further evidence in support of the conjecture that the distribution of the eigenmatrix of $S_n$ is asymptotically close to that of a Haar-distributed unitary matrix.Comment: Published in at http://dx.doi.org/10.1214/10-AAP748 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inference and Optimization of Real Edges on Sparse Graphs - A Statistical Physics Perspective

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge-variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods are established. Different cost measures are considered and algorithmic solutions in the various cases are devised and examined numerically. Simulation results are in full agreement with the theory.Comment: 21 pages, 10 figures, major changes: Sections IV to VII updated, Figs. 1 to 3 replace

Models of Financial Markets with Extensive Participation Incentives

We consider models of financial markets in which all parties involved find incentives to participate. Strategies are evaluated directly by their virtual wealths. By tuning the price sensitivity and market impact, a phase diagram with several attractor behaviors resembling those of real markets emerge, reflecting the roles played by the arbitrageurs and trendsetters, and including a phase with irregular price trends and positive sums. The positive-sumness of the players' wealths provides participation incentives for them. Evolution and the bid-ask spread provide mechanisms for the gain in wealth of both the players and market-makers. New players survive in the market if the evolutionary rate is sufficiently slow. We test the applicability of the model on real Hang Seng Index data over 20 years. Comparisons with other models show that our model has a superior average performance when applied to real financial data.Comment: 17 pages, 16 figure

Generation of the auroral kilometric radiation

For abstract, see A82-3554

Elliptic Flow from a Transversally Thermalized Fireball

The agreement of elliptic flow data at RHIC at central rapidity with the hydrodynamic model has led to the conclusion of very rapid thermalization. This conclusion is based on the intuitive argument that hydrodynamics, which assumes instantaneous local thermalization, produces the largest possible elliptic flow values and that the data seem to saturate this limit. We here investigate the question whether incompletely thermalized viscous systems may actually produce more elliptic flow than ideal hydrodynamics. Motivated by the extremely fast primordial longitudinal expansion of the reaction zone, we investigate a toy model which exhibits thermalization only in the transverse directions but undergoes collisionless free-streaming expansion in the longitudinal direction. For collisions at RHIC energies, elliptic flow results from the model are compared with those from hydrodynamics. With the final particle yield and \kt-distribution fixed, the transversally thermalized model is shown not to be able to produce the measured amount of elliptic flow. This investigation provides further support for very rapid local kinetic equilibration at RHIC. It also yields interesting novel results for the elliptic flow of massless particles such as direct photons.Comment: revtex4, 15 pages + 10 embedded EPS figure

A novel approach to non-segmented flow analysis: Part 4. Aluminium in river waters

A rapid and precise method is developed for the determination of aluminium in water. The results demonstrate that the calibration range of the assay can be extended by a simple manipulation of the control program of the flow analyser. An RSD of 1.8% is achieved for injection of standards and the theoretical limit of detection is estimated at 0.33 ppm alum (equivalent to 18 ppb Al3+). The method is applied to monitoring of environmental samples

Current-Induced Spin Polarization in Gallium Nitride

Electrically generated spin polarization is probed directly in bulk GaN using Kerr rotation spectroscopy. A series of n-type GaN epilayers are grown in the wurtzite phase both by molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition (MOCVD) with a variety of doping densities chosen to broadly modulate the transverse spin lifetime, T2*. The spin polarization is characterized as a function of electrical excitation energy over a range of temperatures. Despite weak spin-orbit interactions in GaN, a current-induced spin polarization (CISP) is observed in the material at temperatures of up to 200 K.Comment: 16 pages, 3 figure

Pion Interferometry for Hydrodynamical Expanding Source with a Finite Baryon Density

We calculate the two-pion correlation function for an expanding hadron source with a finite baryon density. The space-time evolution of the source is described by relativistic hydrodynamics and the Hanbury-Brown-Twiss (HBT) radius is extracted after effects of collective expansion and multiple scattering on the HBT interferometry have been taken into account, using quantum probability amplitudes in a path-integral formalism. We find that this radius is substantially smaller than the HBT radius extracted from the freeze-out configuration.Comment: 4 pages, 2 figure

Quantum kinetic description of Coulomb effects in one-dimensional nano-transistors

In this article, we combine the modified electrostatics of a one-dimensional transistor structure with a quantum kinetic formulation of Coulomb interaction and nonequilibrium transport. A multi-configurational self-consistent Green's function approach is presented, accounting for fluctuating electron numbers. On this basis we provide a theory for the simulation of electronic transport and quantum charging effects in nano-transistors, such as gated carbon nanotube and whisker devices and one-dimensional CMOS transistors. Single-electron charging effects arise naturally as a consequence of the Coulomb repulsion within the channel