Bessel processes, the Brownian snake and super-Brownian motion

We prove that, both for the Brownian snake and for super-Brownian motion in dimension one, the historical path corresponding to the minimal spatial position is a Bessel process of dimension -5. We also discuss a spine decomposition for the Brownian snake conditioned on the minimizing path.Comment: Submitted to the special volume of S\'eminaire de Probabilit\'es in memory of Marc Yo

The CANADA-FRANCE REDSHIFT SURVEY XIII: The luminosity density and star-formation history of the Universe to z ~ 1

The comoving luminosity density of the Universe is estimated from the CFRS faint galaxy sample in three wavebands (2800A, 4400A and 1 micron) over the redshift range 0 < z < 1. In all three wavebands, the comoving luminosity density increases markedly with redshift. For a (q_0 = 0.5, Omega = 1.0) cosmological model, the comoving luminosity density increases as $(1+z)^{2.1 \pm 0.5}$ at 1 micron, as $(1+z)^{2.7 \pm 0.5}$ at 4400A and as $(1+z)^{3.9 \pm 0.75}$ at 2800A, these exponents being reduced by 0.43 and 1.12 for (0.05,0.1) and (-0.85,0.1) cosmological models respectively. The variation of the luminosity density with epoch can be reasonably well modelled by an actively evolving stellar population with a Salpeter initial mass function (IMF) extending to 125 M_sun, a star-formation rate declining with a power 2.5, and a turn-on of star-formation at early epochs. A Scalo (1986) IMF extending to the same mass limit produces too many long-lived low mass stars. This rapid evolution of the star-formation rate and comoving luminosity density of the Universe is in good agreement with the conclusions of Pei and Fall (1995) from their analysis of the evolving metallicity of the Universe. One consequence of this evolution is that the physical luminosity density at short wavelengths has probably declined by two orders of magnitude since z ~ 1.Comment: uuencoded compressed tar file containing 8 page Tex file, 2 postscript figures and 2 tables. Ap J Letters, in press. Also available at http://www.astro.utoronto.ca/~lilly/CFRS/papers.htm

Observation of correlations up to the micrometer scale in sliding charge-density waves

High-resolution coherent x-ray diffraction experiment has been performed on the charge density wave (CDW) system K$_{0.3}$MoO$_3$. The $2k_F$ satellite reflection associated with the CDW has been measured with respect to external dc currents. In the sliding regime, the $2k_F$ satellite reflection displays secondary satellites along the chain axis which corresponds to correlations up to the micrometer scale. This super long range order is 1500 times larger than the CDW period itself. This new type of electronic correlation seems inherent to the collective dynamics of electrons in charge density wave systems. Several scenarios are discussed.Comment: 4 pages, 3 figures Typos added, references remove

Valence Quark Spin Distribution Functions

The hyperfine interactions of the constituent quark model provide a natural explanation for many nucleon properties, including the Delta-N splitting, the charge radius of the neutron, and the observation that the proton's quark distribution function ratio d(x)/u(x)->0 as x->1. The hyperfine-perturbed quark model also makes predictions for the nucleon spin-dependent distribution functions. Precision measurements of the resulting asymmetries A_1^p(x) and A_1^n(x) in the valence region can test this model and thereby the hypothesis that the valence quark spin distributions are "normal".Comment: 16 pages, 2 Postscript figure

Cluster Mass Estimate and a Cusp of the Mass Density Distribution in Clusters of Galaxies

We study density cusps in the center of clusters of galaxies to reconcile X-ray mass estimates with gravitational lensing masses. For various mass density models with cusps we compute X-ray surface brightness distribution, and fit them to observations to measure the range of parameters in the density models. The Einstein radii estimated from these density models are compared with Einstein radii derived from the observed arcs for Abell 2163, Abell 2218, and RX J1347.5-1145. The X-ray masses and lensing masses corresponding to these Einstein radii are also compared. While steeper cusps give smaller ratios of lensing mass to X-ray mass, the X-ray surface brightnesses estimated from flatter cusps are better fits to the observations. For Abell 2163 and Abell 2218, although the isothermal sphere with a finite core cannot produce giant arc images, a density model with a central cusp can produce a finite Einstein radius, which is smaller than the observed radii. We find that a total mass density profile which declines as $\sim r^{-1.4}$ produces the largest radius in models which are consistent with the X-ray surface brightness profile. As the result, the extremely large ratio of the lensing mass to the X-ray mass is improved from 2.2 to 1.4 for Abell 2163, and from 3 to 2.4 for Abell 2218. For RX J1347.5-1145, which is a cooling flow cluster, we cannot reduce the mass discrepancy.Comment: 23 pages, 10 figures, Latex, uses aasms4.sty, accepted for publication in ApJ, Part

The perimeter of large planar Voronoi cells: a double-stranded random walk

Let $p\_n$ be the probability for a planar Poisson-Voronoi cell to have exactly $n$ sides. We construct the asymptotic expansion of $\log p\_n$ up to terms that vanish as $n\to\infty$. We show that {\it two independent biased random walks} executed by the polar angle determine the trajectory of the cell perimeter. We find the limit distribution of (i) the angle between two successive vertex vectors, and (ii) the one between two successive perimeter segments. We obtain the probability law for the perimeter's long wavelength deviations from circularity. We prove Lewis' law and show that it has coefficient 1/4.Comment: Slightly extended version; journal reference adde

Sum rules in the heavy quark limit of QCD

In the leading order of the heavy quark expansion, we propose a method within the OPE and the trace formalism, that allows to obtain, in a systematic way, Bjorken-like sum rules for the derivatives of the elastic Isgur-Wise function $\xi(w)$ in terms of corresponding Isgur-Wise functions of transitions to excited states. A key element is the consideration of the non-forward amplitude, as introduced by Uraltsev. A simplifying feature of our method is to consider currents aligned along the initial and final four-velocities. As an illustration, we give a very simple derivation of Bjorken and Uraltsev sum rules. On the other hand, we obtain a new class of sum rules that involve the products of IW functions at zero recoil and IW functions at any $w$. Special care is given to the needed derivation of the projector on the polarization tensors of particles of arbitrary integer spin. The new sum rules give further information on the slope $\rho^2 = - \xi '(1)$ and also on the curvature $\sigma^2 = \xi '' (1)$, and imply, modulo a very natural assumption, the inequality $\sigma^2 \geq {5\over 4} \rho^2$, and therefore the absolute bound $\sigma^2 \geq {15 \over 16}$.Comment: 64 pages, Late

Direct Measurement of the Photon Statistics of a Triggered Single Photon Source

We studied intensity fluctuations of a single photon source relying on the pulsed excitation of the fluorescence of a single molecule at room temperature. We directly measured the Mandel parameter Q(T) over 4 orders of magnitude of observation timescale T, by recording every photocount. On timescale of a few excitation periods, subpoissonian statistics is clearly observed and the probablility of two-photons events is 10 times smaller than Poissonian pulses. On longer times, blinking in the fluorescence, due to the molecular triplet state, produces an excess of noise.Comment: 4 pages, 3 figures, 1 table submitted to Physical Review Letter