The Market for Preclusion in Merger Litigation

The recent finding that corporate litigation involving Delaware companies very often takes place outside of Delaware has disturbed the long-settled understanding of how merger litigation works. With many, even most, cases being filed and ultimately resolved outside of Delaware, commentators warn that the trend is a threat to shareholders, to Delaware, and to the integrity of corporate law generally. Although the out-of-Delaware trend suggests that litigants are seeking to use the procedural rules of other jurisdictions to their advantage, we argue that the result need not threaten the interests of any of the stakeholders in deal litigation. We reframe the process of resolving merger litigation as a market for preclusion, in which plaintiffs seek to sell and defendants seek to buy an important element of transactional certainty. Moreover, this market has the potential to efficiently process and price shareholder complaints while also providing benefits to Delaware and to corporate law more generally. We are not blind to reality, however, and also address how a well-functioning market for preclusion can be distorted by the opportunistic conduct of plaintiffs’ and defense attorneys alike. Greater judicial oversight is necessary to preserve the benefits of this market while preventing the distortions brought on through opportunistic conduct. In order to make this a reality, however, judges in different courts must have a means of communicating and coordinating across state lines. We therefore offer a theory of horizontal comity in which judges build trust and cooperation through communication across jurisdictional boundaries. We use this theory to suggest a set of concrete policy proposals designed to provide for a more efficient market for preclusion

The correlation function of radio sources

We investigate the large-scale clustering of radio sources in the Green Bank and Parkes-MIT-NRAO 4.85 GHz surveys by measuring the angular two-point correlation function w(\theta). Excluding contaminated areas, the two surveys together cover 70 per cent of the whole sky. We find both surveys to be reasonably complete above 50 mJy. On the basis of previous studies, the radio sources are galaxies and radio-loud quasars lying at redshifts up to z \sim 4, with a median redshift z \sim 1. This provides the opportunity to probe large-scale structures in a volume far larger than that within the reach of present optical and infrared surveys. We detect a clustering signal w(\theta) \approx 0.01 for \theta = 1\degr. By assuming an evolving power-law spatial correlation function in comoving coordinates \xi(r_c,z) = ( r_c / r_0 )^{-\gamma} (1+z)^{\gamma-(3+\epsilon)}, where \gamma = 1.8, and the redshift distribution N(z) of the radio galaxies, we constrain the r_0--\epsilon parameter space. For `stable clustering' (\epsilon = 0), we find the correlation length r_0 \approx 18 Mpc/h, larger than the value for nearby normal galaxies and comparable to the cluster-cluster correlation length.Comment: 8 pages, 7 ps figures included, LaTeX (mn,sty). Accepted by MNRA

Do galactic potential wells depend on their environment?

Using galaxies in complete samples as tracers of the galaxy density field and about 1000 galaxies with measured circular velocities as targets, we examine the cross-correlation functions between the targets and tracers as a function of galaxy circular velocities. The correlation strength does not vary with the circular velocities except for elliptical galaxies with the highest velocity dispersions, where the effect may well be due to morphological segregations in clusters of galaxies. This is contrasted with the strong dependence of the correlation functions of dark halos on their circular velocities in some models of galaxy formation

Variance and Skewness in the FIRST survey

We investigate the large-scale clustering of radio sources in the FIRST 1.4-GHz survey by analysing the distribution function (counts in cells). We select a reliable sample from the the FIRST catalogue, paying particular attention to the problem of how to define single radio sources from the multiple components listed. We also consider the incompleteness of the catalogue. We estimate the angular two-point correlation function $w(\theta)$, the variance $\Psi_2$, and skewness $\Psi_3$ of the distribution for the various sub-samples chosen on different criteria. Both $w(\theta)$ and $\Psi_2$ show power-law behaviour with an amplitude corresponding a spatial correlation length of $r_0 \sim 10 h^{-1}$Mpc. We detect significant skewness in the distribution, the first such detection in radio surveys. This skewness is found to be related to the variance through $\Psi_3=S_3(\Psi_2)^{\alpha}$, with $\alpha=1.9\pm 0.1$, consistent with the non-linear gravitational growth of perturbations from primordial Gaussian initial conditions. We show that the amplitude of variance and skewness are consistent with realistic models of galaxy clustering.Comment: 13 pages, 21 inline figures, to appear in MNRA

Searching for Large Scale Structure in Deep Radio Surveys

(Abridged Abstract) We calculate the expected amplitude of the dipole and higher spherical harmonics in the angular distribution of radio galaxies. The median redshift of radio sources in existing catalogues is z=1, which allows us to study large scale structure on scales between those accessible to present optical and infrared surveys, and that of the Cosmic Microwave Background (CMB). The dipole is due to 2 effects which turn out to be of comparable magnitude: (i) our motion with respect to the CMB, and (ii) large scale structure, parameterised here by a family of Cold Dark Matter power-spectra. We make specific predictions for the Green Bank (87GB) and Parkes-MIT-NRAO (PMN) catalogues. For these relatively sparse catalogues both the motion and large scale structure dipole effects are expected to be smaller than the Poisson shot-noise. However, we detect dipole and higher harmonics in the combined 87GB-PMN catalogue which are far larger than expected. We attribute this to a 2 % flux mismatch between the two catalogues. We also investigate the existence and extent of the Supergalactic Plane in the above catalogues. In a strip of +- 10 deg of the standard Supergalactic equator, we find a 3-sigma detection in PMN, but only 1-sigma in 87GB.Comment: 15 pages, 5 ps figures, Latex, Submitted to MNRA

The 2dF gravitational lens survey

The 2 degree Field (2dF) galaxy redshift survey will involve obtaining approximately 2.5 x 10^5 spectra of objects previously identified as galaxy candidates on morphological grounds. Included in these spectra should be about ten gravitationally-lensed quasars, all with low-redshift galaxies as deflectors (as the more common lenses with high-redshift deflectors will be rejected from the survey as multiple point-sources). The lenses will appear as superpositions of galaxy and quasar spectra, and both cross-correlation techniques and principal components analysis should be able to identify candidates systematically. With the 2dF survey approximately half-completed it is now viable to begin a systematic search for these spectroscopic lenses, and the first steps of this project are described here.Comment: PASA (OzLens edition), in press; 4 pages, 0 figure

The X-ray Cluster Dipole

We estimate the dipole of the whole sky X-ray flux-limited sample of Abell/ACO clusters (XBACs) and compare it to the optical Abell/ACO cluster dipole. The X-ray cluster dipole is well aligned ($\le 25^{\circ}$) with the CMB dipole, while it follows closely the radial profile of its optical cluster counterpart although its amplitude is $\sim 10 - 30$ per cent lower. In view of the fact that the the XBACs sample is not affected by the volume incompleteness and the projection effects that are known to exist at some level in the optical parent Abell/ACO cluster catalogue, our present results confirm the previous optical cluster dipole analysis that there are significant contributions to the Local Group motion from large distances ($\sim 160h^{-1}$Mpc). In order to assess the expected contribution to the X-ray cluster dipole from a purely X-ray selected sample we compare the dipoles of the XBACs and the Brightest Cluster Sample (Ebeling et al. 1997a) in their overlap region. The resulting dipoles are in mutual good aggreement with an indication that the XBACs sample slightly underestimates the full X-ray dipole (by $\le 5$ per cent) while the Virgo cluster contributes about 10 - 15 per cent to the overall X-ray cluster dipole. Using linear perturbation theory to relate the X-ray cluster dipole to the Local group peculiar velocity we estimate the density parameter to be $\beta_{c_{x}} \simeq 0.24 \pm 0.05$.Comment: 16 pages, latex, + 4 ps figures, submitted to Ap

Precision Cosmology? Not Just Yet

The recent announcement from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite experiment combined with other recent advances in observational cosmology verifies key components of the standard cosmological model. However, we argue that there remain some significant open issues regarding the basic history and composition of the Universe and uncertainties in some of the most important parameters.Comment: 2 pages, 2 figures. Online journal version http://www.sciencemag.org/cgi/content/full/299/5612/153

On the Magnitude of Dark Energy Voids and Overdensities

We investigate the clustering of dark energy within matter overdensities and voids. In particular, we derive an analytical expression for the dark energy density perturbations, which is valid both in the linear, quasi-linear and fully non-linear regime of structure formation. We also investigate the possibility of detecting such dark energy clustering through the ISW effect. In the case of uncoupled quintessence models, if the mass of the field is of order the Hubble scale today or smaller, dark energy fluctuations are always small compared to the matter density contrast. Even when the matter perturbations enter the non-linear regime, the dark energy perturbations remain linear. We find that virialised clusters and voids correspond to local overdensities in dark energy, with \delta_{\phi}/(1+w) \sim \Oo(10^{-5}) for voids, \delta_{\phi}/(1+w) \sim \Oo(10^{-4}) for super-voids and \delta_{\phi}/(1+w) \sim \Oo(10^{-5}) for a typical virialised cluster. If voids with radii of $100-300 {\rm Mpc}$ exist within the visible Universe then $\delta_{\phi}$ may be as large as $10^{-3}(1+w)$. Linear overdensities of matter and super-clusters generally correspond to local voids in dark energy; for a typical super-cluster: \delta_{\phi}/(1+w) \sim \Oo(-10^{-5}). The approach taken in this work could be straightforwardly extended to study the clustering of more general dark energy models.Comment: 20 pages, 14 figures. Accepted by the Astrophys.

An Improved Semi-Analytical Spherical Collapse Model for Non-linear Density Evolution

We derive a semi-analytical extension of the spherical collapse model of structure formation that takes account of the effects of deviations from spherical symmetry and shell crossing which are important in the non-linear regime. Our model is designed so that it predicts a relation between the peculiar velocity and density contrast that agrees with the results of N-body simulations in the region where such a comparison can sensibly be made. Prior to turnaround, when the unmodified spherical collapse model is expect to be a good approximation, the predictions of the two models coincide almost exactly. The effects of a late time dominating dark energy component are also taken into account. The improved spherical collapse model is a useful tool when one requires a good approximation not just to the evolution of the density contrast but also its trajectory. Moreover, the analytical fitting formulae presented is simple enough to be used anywhere where the standard spherical collapse might be used but with the advantage that it includes a realistic model of the effects of virialisation.Comment: 6 pages, 3 figures. Matches the version in print at Astrophys.