Broad distribution effects in sums of lognormal random variables

The lognormal distribution describing, e.g., exponentials of Gaussian random variables is one of the most common statistical distributions in physics. It can exhibit features of broad distributions that imply qualitative departure from the usual statistical scaling associated to narrow distributions. Approximate formulae are derived for the typical sums of lognormal random variables. The validity of these formulae is numerically checked and the physical consequences, e.g., for the current flowing through small tunnel junctions, are pointed out.Comment: 14 pages, 9 figures. Minor changes + Gini coefficient and 4 refs. adde

Twisted Jacobi manifolds, twisted Dirac-Jacobi structures and quasi-Jacobi bialgebroids

We study twisted Jacobi manifolds, a concept that we had introduced in a previous Note. Twisted Jacobi manifolds can be characterized using twisted Dirac-Jacobi, which are sub-bundles of Courant-Jacobi algebroids. We show that each twisted Jacobi manifold has an associated Lie algebroid with a 1-cocycle. We introduce the notion of quasi-Jacobi bialgebroid and we prove that each twisted Jacobi manifold has a quasi-Jacobi bialgebroid canonically associated. Moreover, the double of a quasi-Jacobi bialgebroid is a Courant-Jacobi algebroid. Several examples of twisted Jacobi manifolds and twisted Dirac-Jacobi structures are presented

Zero-temperature TAP equations for the Ghatak-Sherrington model

The zero-temperature TAP equations for the spin-1 Ghatak-Sherrington model are investigated. The spin-glass energy density (ground state) is determined as a function of the anisotropy crystal field $D$ for a large number of spins. This allows us to locate a first-order transition between the spin-glass and paramagnetic phases within a good accuracy. The total number of solutions is also determined as a function of $D$.Comment: 11 pages, 2 ps figures include

Effects of Random Biquadratic Couplings in a Spin-1 Spin-Glass Model

A spin-1 model, appropriated to study the competition between bilinear (J_{ij}S_{i}S_{j}) and biquadratic (K_{ij}S_{i}^{2}S_{j}^{2}) random interactions, both of them with zero mean, is investigated. The interactions are infinite-ranged and the replica method is employed. Within the replica-symmetric assumption, the system presents two phases, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic couplings between the spins.Comment: 16 pages plus 2 ps figure

Building a Sample of Distant Clusters of Galaxies

Candidate clusters of galaxies drawn from the sample identified from the moderately deep I-band data of the ESO Imaging Survey (EIS), have been used for follow-up optical/infrared imaging and spectroscopic observations. The observations were conducted to assess the nature of these candidates over a large range of redshifts. Currently, 163 EIS candidates have (V-I) colors, 15 have (I-K) and 65 cluster fields have been observed spectroscopically. From a preliminary analysis of these data, we find that > 65% of the candidates studied show strong evidence of being real physical associations, over the redshift range 0.2<z<1.1. The evidence in some cases comes directly from spectroscopic measurements, in others indirectly from the detection of overdensities of objects with either the same color or the same photometric redshift, or from a combination of color and spectroscopic information. Preliminary results also suggest that the redshift derived from the matched-filter algorithm is a reasonable measure of the cluster's redshift, possibly overestimating it by Delta z ~0.1, at least for systems at z<0.7. Overdensities of red objects have been detected in over 100 candidates, 38 of which with estimated redshifts >0.6, and six candidates in the interval 0.45<z<0.81 have either been identified directly from measured redshifts or have been confirmed by the measurement of at least one redshift for galaxies located along a red-sequence typical of cluster early-type galaxies. Lastly, five candidates among those already observed in the infrared have (I-Ks) colors consistent with them being in the redshift interval 0.8<z<1.1. The sample of "confirmed" clusters, already the largest of its kind in the southern hemisphere, will be further enlarged by ongoing observations.Comment: To appear in "Large Scale Structure in the X-ray Universe", ed. M. Plionis and I. Georgantopoulos (Paris: Editions Frontieres), in pres