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

Elastic α\alpha-transfer in the elastic scattering of 16^{\bf 16}O+12+^{\bf 12}C

The elastic scattering $^{16}$O$+^{12}$C angular distributions at $^{16}$O bombarding energies of 100.0, 115.9 and 124.0 MeV and their optical model description including the $\alpha$-particle exchange contribution calculated in the Coupled Reaction Channel approach are presented. The angular distributions show not only the usual diffraction pattern but also, at larger angles, intermediate structure of refractive origin on which finer oscillations are superimposed. The large angle features can be consistently described including explicitly the elastic $\alpha$-transfer process and using a refractive optical potential with a deep real part and a weakly absorptive imaginary part.Comment: 3 pages, 2 figures, accepted in Eur.Phys.J A (Short note

Fusion excitation function revisited

We report on a comprehensive systematics of fusion-evaporation and/or fusion-fission cross sections for a very large variety of systems over an energy range 4-155 A.MeV. Scaled by the reaction cross sections, fusion cross sections do not show a universal behavior valid for all systems although a high degree of correlation is present when data are ordered by the system mass asymmetry.For the rather light and close to mass-symmetric systems the main characteristics of the complete and incomplete fusion excitation functions can be precisely determined. Despite an evident lack of data above 15A.MeV for all heavy systems the available data suggests that geometrical effects could explain the persistence of incomplete fusion at incident energies as high as 155A.MeV.Comment: 8 pages, 5 figures, contribution to the NN2012 Proceeding