Expected Supremum of a Random Linear Combination of Shifted Kernels

We address the expected supremum of a linear combination of shifts of the sinc kernel with random coefficients. When the coefficients are Gaussian, the expected supremum is of order \sqrt{\log n}, where n is the number of shifts. When the coefficients are uniformly bounded, the expected supremum is of order \log\log n. This is a noteworthy difference to orthonormal functions on the unit interval, where the expected supremum is of order \sqrt{n\log n} for all reasonable coefficient statistics.Comment: To appear in the Journal of Fourier Analysis and Application

Intervening Metal Systems in GRB and QSO sight-lines: The Mgii and Civ Question

Prochter et al. 2006 recently found that the number density of strong intervening 0.5<z<2 MgII absorbers detected in gamma-ray burst (GRB) afterglow spectra is nearly 4 times larger than in QSO spectra. We have conducted a similar study using CIV absorbers. Our CIV sample, consisting of a total of 20 systems, is drawn from 3 high resolution and high to moderate S/N VLT/UVES spectra of 3 long-duration GRB afterglows, covering the redshift interval 1.6< z<3.1. The column density distribution and number density of this sample do not show any statistical difference with the same quantities measured in QSO spectra. We discuss several possibilities for the discrepancy between CIV and MgII absorbers and conclude that a higher dust extinction in the MgII QSO samples studied up to now would give the most straightforward solution. However, this effect is only important for the strong MgII absorbers. Regardless of the reasons for this discrepancy, this result confirms once more that GRBs can be used to detect a side of the universe that was unknown before, not necessarily connected with GRBs themselves, providing an alternative and fundamental investigative tool of the cosmic evolution of the universe.Comment: 21 pages, 4 figures, ApJ accepted, Revised after Referee Repor

A translucent interstellar cloud at z=2.69: CO, H2 and HD in the line-of-sight to SDSS J123714.60+064759.5

We present the analysis of a sub-DLA system (log N(H^0)=20.0+/-0.15, z_abs=2.69) toward SDSS J123714+064759 (z_em=2.78). Using the VLT/UVES and X-shooter spectrographs, we detect H2, HD and CO molecules in absorption with log N(H2,HD,CO)=(19.21,14.48,14.17). The overall metallicity of the system is super-solar ([Zn/H]=+0.34) and iron is highly depleted ([Fe/Zn]=-1.39), revealing metal-rich and dusty gas. The strongest H2 component does not coincide with the centre of the HI absorption. This implies that the molecular fraction in this component, f=2N(H2)/(2N(H2)+N(H^0)), is larger than the mean molecular fraction =1/4 in the system. This is supported by the detection of Cl^0 associated with this H2-component having N(Cl^0)/N(Cl^+)>0.4. Since Cl^0 is tied up to H2 by charge exchange reactions, this means that the molecular fraction in this component is not far from unity. The size of the molecular cloud is probably smaller than 1pc. Both the CO/H2=10^-5 and CO/C^0~1 ratios for f>0.24 indicate that the cloud classifies as translucent, i.e., a regime where carbon is found both in atomic and molecular form. The corresponding extinction, Av=0.14, albeit lower than the definition of a translucent sightline (based on extinction properties), is high for the observed H^0 column density. This means that intervening clouds with similar local properties but with larger column densities could be missed by current magnitude-limited QSO surveys. The excitation of CO is dominated by radiative interaction with the Cosmic Microwave Background Radiation (CMBR) and we derive Tex(CO)=10.5+0.8-0.6 K when TCMBR(z=2.69)=10.05 K is expected. The astration factor of deuterium -with respect to the primordial D/H ratio- is only about 3. This can be the consequence of accretion of unprocessed gas from the intergalactic medium onto the associated galaxy. [abridged]Comment: 17 pages, 21 figures, 8 tables, accepted for publication in A&

Deuterium at high-redshift: Primordial abundance in the zabs = 2.621 damped Ly-alpha system towards CTQ247

The detection of neutral deuterium in the low-metallicity damped Lyman-{\alpha} system at zabs = 2.621 towards the quasar CTQ247 is reported. Using a high signal-to-noise and high spectral resolution (R = 60000) spectrum from the Very Large Telescope Ultraviolet and Visual Echelle Spectrograph, we precisely measure the deuterium-to-oxygen ratio log N(DI)/N(OI) = 0.74+/-0.04, as well as the overall oxygen abundance, log N(OI)/N(HI)=-5.29+/-0.10 (or equivalently [O/H]=-1.99+/-0.10 with respect to the solar value). Assuming uniform metallicity throughout the system, our measurement translates to (D/H) = (2.8+0.8 -0.6)x10^-5. This ratio is consistent within errors (<0.4sigma) with the primordial ratio, (D/H)p = (2.59+/-0.15)x10^-5, predicted by standard Big-Bang Nucleosynthesis using the WMAP7 value of the cosmological density of baryons (100 Omega_b h^2 = 2.249+/-0.056). The DI absorption lines are observed to be broader than the OI absorption lines. From a consistent fit of the profiles we derive the turbulent broadening to be 5.2 km/s and the temperature of the gas to be T = 8800+/-1500 K, corresponding to a warm neutral medium.Comment: Accepted for publication in A&A Letter

On Hastings' counterexamples to the minimum output entropy additivity conjecture

Hastings recently reported a randomized construction of channels violating the minimum output entropy additivity conjecture. Here we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument. Furthermore, we prove non-additivity for the overwhelming majority of channels consisting of a Haar random isometry followed by partial trace over the environment, for an environment dimension much bigger than the output dimension. This makes Hastings' original reasoning clearer and extends the class of channels for which additivity can be shown to be violated.Comment: 17 pages + 1 lin

The Polarized Spectrum of Apm 08279+5255

We report the discovery of significant linear polarization (p > 1%) in the hyperluminous z=3.87 BALQSO APM~08279+5255. The polarization spectrum is complex, with properties similar to those of other, lower redshift but more highly polarized BALQSOs. The resonance emission lines are unpolarized while the absorption troughs show polarization similar to or higher than the continuum. In particular, an apparent increase of polarization in the trough covering 1000-1030 angstroms (rest) supports the interpretation of this feature as a broad absorption component associated with OVI/Ly_beta local to the QSO, as opposed to an intervening damped Ly_alpha absorption system. The elevated polarization in some of the absorption features implies that we view the scattered (polarized) spectrum through a sightline with less absorbing material than the direct spectrum. Therefore, the complex structure of the polarization spectrum in this brilliant lensed BALQSO suggests that it will be an important laboratory for studying the structure of QSOs at high redshift.Comment: 8 pages, 1 figure. Accepted for publication in The Astrophysical Journal Letter

A prototype ASIC for APD array readout of scintillating plastic fibers

We report on the development of custom front-end electronics for use with avalanche photodiode (APD) arrays as part of a NASA technology study for the readout of scintillating plastic fibers. APD arrays featuring 64 1 mm square pixels are used. We demonstrate that a pixel of these APD arrays coupled to relatively thin (0.25 mm) and short (15 cm) scintillating plastic fibers can be used to detect and measure the tracks of even minimum ionizing particles (MIPs). An applicationspecific integrated circuit (ASIC) implementation of the electronics is required to produce a detector sufficiently compact for practical use in a flight experiment featuring many thousands of channels. This paper briefly describes the detector concept and performance and presents the design and performance of a four-channel prototype ASIC fabricated using the 0.35 micron TSMC process

CO-dark molecular gas at high redshift: very large H2_2 content and high pressure in a low metallicity damped Lyman-alpha system

We present a detailed analysis of a H$_2$-rich, extremely strong intervening Damped Ly-$\alpha$ Absorption system (DLA) at $z_{\rm abs}=2.786$ towards the quasar J$\,$0843+0221, observed with the Ultraviolet and Visual Echelle Spectrograph on the Very Large Telescope. The total column density of molecular (resp. atomic) hydrogen is $\log N$(H$_2$)=$21.21\pm0.02$ (resp. $\log N$(H$\,$I)=$21.82\pm0.11$), making it to be the first case in quasar absorption lines studies with H$_2$ column density as high as what is seen in $^{13}$CO-selected clouds in the Milky-Way. We find that this system has one of the lowest metallicity detected among H$_2$-bearing DLAs, with $\rm [Zn/H]=-1.52^{+0.08}_{-0.10}$. This can be the reason for the marked differences compared to systems with similar H$_2$ column densities in the local Universe: $(i)$ the kinetic temperature, $T\sim$120~K, derived from the $J=0,1$ H$_2$ rotational levels is at least twice higher than expected; $(ii)$ there is little dust extinction with A$_V < 0.1$; $(iii)$ no CO molecules are detected, putting a constraint on the $X_{\rm CO}$ factor $X_{\rm CO}> 2\times 10^{23}$ cm$^{-2}$/(km/s\,K), in the very low metallicity gas. Low CO and high H$_2$ contents indicate that this system represents "CO-dark/faint" gas. We investigate the physical conditions in the H$_2$-bearing gas using the fine-structure levels of C$\,$I, C$\,$II, Si$\,$II and the rotational levels of HD and H$_2$. We find the number density to be about $n \sim 260-380\,$cm$^{-3}$, implying a high thermal pressure of $(3-5) \times 10^4\,$cm$^{-3}\,$K. We further identify a trend of increasing pressure with increasing total hydrogen column density. This independently supports the suggestion that extremely strong DLAs (with $\log\,$N(H) $\sim 22$) probe high-z galaxies at low impact parameters.Comment: 21 pages, 21 figures. Accepted for publication in MNRA

The central limit problem for random vectors with symmetries

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein's method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry and we give a brief introduction to the classical method. The spherically symmetric case is treated by a variation of Stein's method which is adapted for continuous symmetries.Comment: AMS-LaTeX, uses xy-pic, 23 pages; v3: added new corollary to Theorem

Monsters, black holes and the statistical mechanics of gravity

We review the construction of monsters in classical general relativity. Monsters have finite ADM mass and surface area, but potentially unbounded entropy. From the curved space perspective they are objects with large proper volume that can be glued on to an asymptotically flat space. At no point is the curvature or energy density required to be large in Planck units, and quantum gravitational effects are, in the conventional effective field theory framework, small everywhere. Since they can have more entropy than a black hole of equal mass, monsters are problematic for certain interpretations of black hole entropy and the AdS/CFT duality. In the second part of the paper we review recent developments in the foundations of statistical mechanics which make use of properties of high-dimensional (Hilbert) spaces. These results primarily depend on kinematics -- essentially, the geometry of Hilbert space -- and are relatively insensitive to dynamics. We discuss how this approach might be adopted as a basis for the statistical mechanics of gravity. Interestingly, monsters and other highly entropic configurations play an important role.Comment: 9 pages, 4 figures, revtex; invited Brief Review to be published in Modern Physics Letters