Identifying topological-band insulator transitions in silicene and other 2D gapped Dirac materials by means of R\'enyi-Wehrl entropy

We propose a new method to identify transitions from a topological insulator to a band insulator in silicene (the silicon equivalent of graphene) in the presence of perpendicular magnetic and electric fields, by using the R\'enyi-Wehrl entropy of the quantum state in phase space. Electron-hole entropies display an inversion/crossing behavior at the charge neutrality point for any Landau level, and the combined entropy of particles plus holes turns out to be maximum at this critical point. The result is interpreted in terms of delocalization of the quantum state in phase space. The entropic description presented in this work will be valid in general 2D gapped Dirac materials, with a strong intrinsic spin-orbit interaction, isoestructural with silicene.Comment: to appear in EP

Copulas in finance and insurance

Copulas provide a potential useful modeling tool to represent the dependence structure among variables and to generate joint distributions by combining given marginal distributions. Simulations play a relevant role in finance and insurance. They are used to replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so on. Using copulas, it is easy to construct and simulate from multivariate distributions based on almost any choice of marginals and any type of dependence structure. In this paper we outline recent contributions of statistical modeling using copulas in finance and insurance. We review issues related to the notion of copulas, copula families, copula-based dynamic and static dependence structure, copulas and latent factor models and simulation of copulas. Finally, we outline hot topics in copulas with a special focus on model selection and goodness-of-fit testing

Searching for pairing energies in phase space

We obtain a representation of pairing energies in phase space, for the Lipkin-Meshkov-Glick and general boson Bardeen-Cooper-Schrieffer pairing models. This is done by means of a probability distribution of the quantum state in phase space. In fact, we prove a correspondence between the points at which this probability distribution vanishes and the pairing energies. In principle, the vanishing of this probability distribution is experimentally accessible and additionally gives a method to visualize pairing energies across the model control parameter space. This result opens new ways to experimentally approach quantum pairing systems.Comment: 5 pages, 4 figure

Copulas in finance and insurance

Copulas provide a potential useful modeling tool to represent the dependence structure among variables and to generate joint distributions by combining given marginal distributions. Simulations play a relevant role in finance and insurance. They are used to replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so on. Using copulas, it is easy to construct and simulate from multivariate distributions based on almost any choice of marginals and any type of dependence structure. In this paper we outline recent contributions of statistical modeling using copulas in finance and insurance. We review issues related to the notion of copulas, copula families, copula-based dynamic and static dependence structure, copulas and latent factor models and simulation of copulas. Finally, we outline hot topics in copulas with a special focus on model selection and goodness-of-fit testing.Dependence structure, Extremal values, Copula modeling, Copula review

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, I

36 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.-- Part II of this paper published in: Approx. Theory Appl. 18(2): 1-32 (2002), available at: http://e-archivo.uc3m.es/handle/10016/6483MR#: MR2047389 (2005k:42062)Zbl#: Zbl 1081.42024In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measure and find general conditions under which these spaces are complete. These results have important consequences in approximation theory. We also find conditions under which the evaluation operator is bounded.Research by first (J.M.R.), third (E.R.) and fourth (D.P.) authors was partially supported by a grant from DGI (BFM 2000-0206-C04-01), Spain.Publicad