On-site correlation in valence and core states of ferromagnetic nickel

We present a method which allows to include narrow-band correlation effects into the description of both valence and core states and we apply it to the prototypical case of nickel. The results of an ab-initio band calculation are used as input mean-field eigenstates for the calculation of self-energy corrections and spectral functions according to a three-body scattering solution of a multi-orbital Hubbard hamiltonian. The calculated quasi-particle spectra show a remarkable agreement with photoemission data in terms of band width, exchange splitting, satellite energy position of valence states, spin polarization of both the main line and the satellite of the 3p core level.Comment: 14 pages, 10 PostScript figures, RevTeX, submitted to PR

A functional limit theorem for dependent sequences with infinite variance stable limits

Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version of this is known to be true as well, the limit process being a stable L\'{e}vy process. The main result in the paper is that for a stationary, regularly varying sequence for which clusters of high-threshold excesses can be broken down into asymptotically independent blocks, the properly centered partial sum process still converges to a stable L\'{e}vy process. Due to clustering, the L\'{e}vy triple of the limit process can be different from the one in the independent case. The convergence takes place in the space of c\`{a}dl\`{a}g functions endowed with Skorohod's $M_1$ topology, the more usual $J_1$ topology being inappropriate as the partial sum processes may exhibit rapid successions of jumps within temporal clusters of large values, collapsing in the limit to a single jump. The result rests on a new limit theorem for point processes which is of independent interest. The theory is applied to moving average processes, squared GARCH(1,1) processes and stochastic volatility models.Comment: Published in at http://dx.doi.org/10.1214/11-AOP669 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Cosmology under Milne's shadow

Based on the magnitude--redshift diagram for the sample of supernovae Ia analysed by Perlmutter et al. (1999), Davis & Lineweaver rule out the special relativistic interpretation of cosmological redshifts at a confidence level of 23 sigma. Here, we critically reassess this result. Special relativity is known to describe the dynamics of an empty universe, by means of the Milne kinematic model. Applying only special-relativistic concepts, we derive the angular diameter distance and the luminosity distance in the Milne model. In particular, in this model we do not use the underlying metric in its Robertson-Walker form, so our exposition is useful for readers without any knowledge of general relativity. We do however, explicitly use the special-relativistic Doppler formula for redshift. We apply the derived luminosity distance to the magnitude--redshift diagram for supernovae Ia of Perlmutter et al. (1999) and show that special relativity fits the data much better than that claimed by Davis & Lineweaver. Specifically, using these data alone, the Milne model is ruled out only at a 2 sigma level. Although not a viable cosmological model, in the context of current research on supernovae Ia it remains a useful reference model when comparing predictions of various cosmological models.Comment: 5 pages, 1 figure; a didactic article; matches the version accepted for publication in PAS

Transition Redshift: New Kinematic Constraints from Supernovae

The transition redshift (deceleration/acceleration) is discussed by expanding the deceleration parameter to first order around its present value. A detailed study is carried out by considering two different parameterizations: $q=q_0 + q_1z$ and $q=q_0 + q_1 z(1+z)^{-1}$, and the associated free parameters ($q_o, q_1$) are constrained by 3 different supernova samples. The previous analysis by Riess {\it{et al.}} [ApJ 607, 665, 2004] using the first expansion is slightly improved and confirmed in light of their recent data ({\emph{Gold}}07 sample). However, by fitting the model with the Supernova Legacy Survey (SNLS) type Ia sample we find that the best fit to the redshift transition is $z_t = 0.61$ instead of $z_t = 0.46$ as derived by the High-z Supernovae Search (HZSNS) team. This result based in the SNLS sample is also in good agreement with the Davis {\it{et al.}} sample, $z_t=0.60^{+0.28}_{-0.11}$ ($1\sigma$). Such results are in line with some independent analyzes and accommodates more easily the concordance flat model ($\Lambda$CDM). For both parameterizations, the three SNe type Ia samples considered favor recent acceleration and past deceleration with a high degree of statistical confidence level. All the kinematic results presented here depend neither on the validity of general relativity nor the matter-energy contents of the Universe.Comment: 19 pages, 15 figures, 1 table, revised version accepted for publication in MNRA

The extremogram: A correlogram for extreme events

We consider a strictly stationary sequence of random vectors whose finite-dimensional distributions are jointly regularly varying with some positive index. This class of processes includes, among others, ARMA processes with regularly varying noise, GARCH processes with normally or Student-distributed noise and stochastic volatility models with regularly varying multiplicative noise. We define an analog of the autocorrelation function, the extremogram, which depends only on the extreme values in the sequence. We also propose a natural estimator for the extremogram and study its asymptotic properties under $\alpha$-mixing. We show asymptotic normality, calculate the extremogram for various examples and consider spectral analysis related to the extremogram.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ213 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm