Extreme Value Theory for Piecewise Contracting Maps with Randomly Applied Stochastic Perturbations

We consider globally invertible and piecewise contracting maps in higher dimensions and we perturb them with a particular kind of noise introduced by Lasota and Mackey. We got random transformations which are given by a stationary process: in this framework we develop an extreme value theory for a few classes of observables and we show how to get the (usual) limiting distributions together with an extremal index depending on the strength of the noise.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1407.041

Statistical stability and limit laws for Rovella maps

We consider the family of one-dimensional maps arising from the contracting Lorenz attractors studied by Rovella. Benedicks-Carleson techniques were used by Rovella to prove that there is a one-parameter family of maps whose derivatives along their critical orbits increase exponentially fast and the critical orbits have slow recurrent to the critical point. Metzger proved that these maps have a unique absolutely continuous ergodic invariant probability measure (SRB measure). Here we use the technique developed by Freitas and show that the tail set (the set of points which at a given time have not achieved either the exponential growth of derivative or the slow recurrence) decays exponentially fast as time passes. As a consequence, we obtain the continuous variation of the densities of the SRB measures and associated metric entropies with the parameter. Our main result also implies some statistical properties for these maps.Comment: 1 figur

A Random Multifractal Tilling

We develop a multifractal random tilling that fills the square. The multifractal is formed by an arrangement of rectangular blocks of different sizes, areas and number of neighbors. The overall feature of the tilling is an heterogeneous and anisotropic random self-affine object. The multifractal is constructed by an algorithm that makes successive sections of the square. At each $n$-step there is a random choice of a parameter $\rho_i$ related to the section ratio. For the case of random choice between $\rho_1$ and $\rho_2$ we find analytically the full spectrum of fractal dimensions

Heavy Color-Octet Particles at the LHC

Many new-physics models, especially those with a color-triplet top-quark partner, contain a heavy color-octet state. The "naturalness" argument for a light Higgs boson requires that the color-octet state be not much heavier than a TeV, and thus it can be pair-produced with large cross sections at high-energy hadron colliders. It may decay preferentially to a top quark plus a top-partner, which subsequently decays to a top quark plus a color-singlet state. This singlet can serve as a WIMP dark-matter candidate. Such decay chains lead to a spectacular signal of four top quarks plus missing energy. We pursue a general categorization of the color-octet states and their decay products according to their spin and gauge quantum numbers. We review the current bounds on the new states at the LHC and study the expected discovery reach at the 8-TeV and 14-TeV runs. We also present the production rates at a future 100-TeV hadron collider, where the cross sections will be many orders of magnitude greater than at the 14-TeV LHC. Furthermore, we explore the extent to which one can determine the color octet's mass, spin, and chiral couplings. Finally, we propose a test to determine whether the fermionic color octet is a Majorana particle.Comment: 20 pages, 9 figures; journal versio

Determining Heavy Mass Parameters in Supersymmetric SO(10) Models

Extrapolations of soft scalar mass parameters in supersymmetric theories can be used to explore elements of the physics scenario near the grand unification scale. We investigate the potential of this method in the lepton sector of SO(10) which incorporates right-handed neutrino superfields. The method is exemplified in two models by exploring limits on the precision that can be expected from coherent LHC and e+e- collider analyses in the reconstruction of the fundamental scalar mass parameters at the unification scale and of the D-terms related to the breaking of grand unification symmetries. In addition, the mass of the third-generation right-handed neutrino can be estimated in seesaw scenarios. Even though the models are simplified and not intended to account for all aspects of a final comprehensive SO(10) theory, they provide nevertheless a valid base for identifying essential elements that can be inferred on the fundamental high-scale theory from high-energy experiments.Comment: 26 pp LaTeX; version published in Phys. Rev.