Point processes and stochastic displacement fields

The effect of a stochastic displacement field on a statistically independent point process is analyzed. Stochastic displacement fields can be divided into two large classes: spatially correlated and uncorrelated. For both cases exact transformation equations for the two-point correlation function and the power spectrum of the point process are found, and a detailed study of them with important paradigmatic examples is done. The results are general and in any dimension. A particular attention is devoted to the kind of large scale correlations that can be introduced by the displacement field, and to the realizability of arbitrary ``superhomogeneous'' point processes.Comment: 17 pages, 7 figure

Chemical etching of a disordered solid: from experiments to field theory

We present a two-dimensional theoretical model for the slow chemical corrosion of a thin film of a disordered solid by suitable etching solutions. This model explain different experimental results showing that the corrosion stops spontaneously in a situation in which the concentration of the etchant is still finite while the corrosion surface develops clear fractal features. We show that these properties are strictly related to the percolation theory, and in particular to its behavior around the critical point. This task is accomplished both by a direct analysis in terms of a self-organized version of the Gradient Percolation model and by field theoretical arguments.Comment: 7 pages, 3 figure

Exponentially spread dynamical Yukawa couplings from non-perturbative chiral symmetry breaking in the dark sector

We propose a new paradigm for generating exponentially spread standard model Yukawa couplings from a new $U(1)_F$ gauge symmetry in the dark sector. Chiral symmetry is spontaneously broken among dark fermions that obtain non-vanishing masses from a non-perturbative solution to the mass gap equation. The necessary ingredient for this mechanism to work is the existence of higher derivative terms in the dark $U(1)_F$ theory, or equivalently the existence of Lee-Wick ghosts, that (i) allow for a non-perturbative solution to the mass gap equation in the weak coupling regime of the Abelian theory; (ii) induce exponential dependence of the generated masses on dark fermion $U(1)_F$ quantum numbers. The generated flavor and chiral symmetry breaking in the dark sector is transferred to the standard model Yukawa couplings at one loop level via Higgs portal type scalar messenger fields. The latter carry quantum numbers of squarks and sleptons. A new intriguing phenomenology is predicted that could be potentially tested at the LHC, provided the characteristic mass scale of the messenger sector is accessible at the LHC as is suggested by naturalness arguments.Comment: Text improved, new equations and references added, version to appear in Phys.Rev.D, 12 pages, 2 figure

Testing Effective Yukawa Couplings in Higgs Searches at the Tevatron and LHC

We explore the possibility that, while the Higgs mechanism provides masses to the weak-gauge bosons at the electroweak scale as in the standard model, fermion masses are generated by an unknown mechanism at a higher energy scale. At low energies, the standard model can then be regarded as an effective field theory, where fermion masses explicitly break the electroweak SU(2)_L \times U(1)_Y gauge symmetry. If \Lambda is the renormalization scale where the renormalized Yukawa couplings vanish, then at energies lower than \Lambda, effective Yukawa couplings will be radiatively induced by nonzero fermion masses. In this scenario, Higgs-boson decays into photons and weak gauge-bosons pairs are in general quite enhanced for a light Higgs. However, depending on \Lambda, a substantial decay rate into b \bar{b} can arise, that can be of the same order as, or larger than, the enhanced H\to gamma gamma rate. A new framework for Higgs searches at hadron colliders is outlined, vector-boson fusion becoming the dominant production mechanism at the CERN LHC, with an important role also played by the WH/ZH associated production. A detailed analysis of the Higgs branching fractions and their implications in Higgs searches is provided, versus the energy scale \Lambda.Comment: 35 pages, 10 figures, 5 tables, Fig.[10] corrected, 1 new reference adde

Peaks in the CMBR power spectrum. I. Mathematical analysis of the associated real space features

The purpose of our study is to understand the mathematical origin in real space of modulated and damped sinusoidal peaks observed in cosmic microwave background radiation anisotropies. We use the theory of the Fourier transform to connect localized features of the two-point correlation function in real space to oscillations in the power spectrum. We also illustrate analytically and by means of Monte Carlo simulations the angular correlation function for distributions of filled disks with fixed or variable radii capable of generating oscillations in the power spectrum. While the power spectrum shows repeated information in the form of multiple peaks and oscillations, the angular correlation function offers a more compact presentation that condenses all the information of the multiple peaks into a localized real space feature. We have seen that oscillations in the power spectrum arise when there is a discontinuity in a given derivative of the angular correlation function at a given angular distance. These kinds of discontinuities do not need to be abrupt in an infinitesimal range of angular distances but may also be smooth, and can be generated by simply distributing excesses of antenna temperature in filled disks of fixed or variable radii on the sky, provided that there is a non-null minimum radius and/or the maximum radius is constrained.Comment: accepted to be published in Physica

The relative importance sector and regional factors in Italy

The benefits of sector and regional diversification have been well documented in the literature but have not previously been investigated in Italy. In addition, previous studies have used geographically defined regions, rather than economically functional areas, when performing the analysis even though most would argue that it is the economic structure of the area that will lead to differences in demand and hence property performance. This study therefore uses economically defined regions of Italy to test the relative benefits of regional diversification versus sector diversification within the Italian real estate portfolio. To examine this issue we use constrained cross-section regressions the on the sector and regional affiliation of 14 cities in Italy to extract the “pure” return effects of the different factors using annual data over the period 1989 to 2003. In contrast, to previous studies we find that regional factors effects in Italy have a much greater influence on property returns than sector-specific effects, which is probably a direct result of using the extremely diverse economic regions of Italy rather than arbitrary geographically locations. Be that as it may, the results strongly suggest that that diversification across the regions of Italy used here is likely to offer larger risk reduction benefits than a sector diversification strategy within a region. In other words, fund managers in Italy must monitor the regional composition of their portfolios more closely than its sector allocation. Additionally, the results supports that contemporary position that ‘regional areas’ based on economic function, provide greater diversification benefits rather than areas defined by geographical location