On the correlation measure of a family of commuting Hermitian operators with applications to particle densities of the quasi-free representations of the CAR and CCR

Let $X$ be a locally compact, second countable Hausdorff topological space. We consider a family of commuting Hermitian operators $a(\Delta)$ indexed by all measurable, relatively compact sets $\Delta$ in $X$ (a quantum stochastic process over $X$). For such a family, we introduce the notion of a correlation measure. We prove that, if the family of operators possesses a correlation measure which satisfies some condition of growth, then there exists a point process over $X$ having the same correlation measure. Furthermore, the operators $a(\Delta)$ can be realized as multiplication operators in the $L^2$-space with respect to this point process. In the proof, we utilize the notion of $\star$-positive definiteness, proposed in [Y. G. Kondratiev and T.\ Kuna, {\it Infin. Dimens. Anal. Quantum Probab. Relat. Top.} {\bf 5} (2002), 201--233]. In particular, our result extends the criterion of existence of a point process from that paper to the case of the topological space $X$, which is a standard underlying space in the theory of point processes. As applications, we discuss particle densities of the quasi-free representations of the CAR and CCR, which lead to fermion, boson, fermion-like, and boson-like (e.g. para-fermions and para-bosons of order 2) point processes. In particular, we prove that any fermion point process corresponding to a Hermitian kernel may be derived in this way

Foreign Reserves and Economic Growth: Granger Causality Analysis with Panel Data

This paper will investigate the Granger causality between foreign reserves and economic growth in twenty largest reserves-holding countries ranging from 1980 to 2008. The method of first-differencing each variable is used to estimate the panel data VAR equations for Granger causality test. The results show the foreign reserves unilaterally Granger cause economic growth only in the emerging countries. In the advanced countries, there is no Granger causal relation between foreign reserves and economic growth.

A Study of Active Galactic Nuclei in Low Surface Brightness Galaxies with Sloan Digital Sky Survey Spectroscopy

Active galactic nuclei (AGN) in low surface brightness galaxies (LSBGs) have received little attention in previous studies. In this paper, we present detailed spectral analysis of 194 LSBGs from the Impey et al. (1996) APM LSBG sample which have been observed spectroscopically by the Sloan Digital Sky Survey Data Release 5 (SDSS DR5). Our elaborate spectral analysis enables us to carry out, for the first time, reliable spectral classification of nuclear activities in LSBGs based on the standard emission line diagnostic diagrams in a rigorous way. Star-forming galaxies are common, as found in about 52% LSBGs. We find, contrary to some of the previous claims, that the fraction of galaxies containing an AGN is significantly lower than that found in nearby normal galaxies of high surface brightness. This is qualitatively in line with the finding of Impey et al. (2001). This result holds true even within each morphological type from Sa to Sc. LSBGs having larger central stellar velocity dispersions, or larger physical sizes, tend to have a higher chance to harbor an AGN. For three AGNs with broad emission lines, the black hole masses estimated from the emission lines are broadly consistent with the well known M-$\sigma_\ast$ relation established for normal galaxies and AGNs.Comment: 5 tables and 14 figure