331 research outputs found
Estimation of the Jump Size Density in a Mixed Compound Poisson Process
International audienceIn this paper, we consider a mixed compound Poisson process, i.e. a random sum of i.i.d. random variables where the number of terms is a Poisson process with random intensity. We study nonparametric estimators of the jump density by specific deconvolution methods. First, assuming that the random intensity has exponential distribution with unknown expectation , we propose two types of estimators based on the observation of an i.i.d. sample. Risks bounds and adaptive procedures are provided. Then, with no assumption on the distribution of the random intensity, we propose two nonparametric estimators of the jump density based on the joint observation of the number of jumps and the random sum of jumps. Risks bounds are provided, leading to unusual rates for one of the two estimators. The methods are implemented and compared via simulations. February 25, 201
Random Fibonacci Sequences
Solutions to the random Fibonacci recurrence x_{n+1}=x_{n} + or - Bx_{n-1}
decrease (increase) exponentially, x_{n} = exp(lambda n), for sufficiently
small (large) B. In the limits B --> 0 and B --> infinity, we expand the
Lyapunov exponent lambda(B) in powers of B and B^{-1}, respectively. For the
classical case of we obtain exact non-perturbative results. In
particular, an invariant measure associated with Ricatti variable
r_n=x_{n+1}/x_{n} is shown to exhibit plateaux around all rational.Comment: 11 Pages (Multi-Column); 3 EPS Figures ; Submitted to J. Phys.
Tectonomagmatic Evolution of Southwestern Laurentia: Insights from Zircon U-Pb Geochronology and Hafnium Isotopic Composition of the Red Bluff Granite Suite, West Texas, USA
We provide laser ablationâmulticollectorâinductively coupled plasmaâmass spectrometry (LA-MC-ICP-MS) and high-precision chemical abrasionâisotope dilutionâthermal ionization mass spectrometry (CA-ID-TIMS) U-Pb ages and Hf isotopic compositions of zircons from the Red Bluff Granite Suite and mafic dikes in the Franklin Mountains of El Paso, Texas, USA. Granitoids exposed in the Franklin Mountains were previously divided into five magmatic stages based on cross-cutting relationships. Major and trace element compositions showed that these granitoids are ferroan, alkaline, and A2 type. Homogeneity in the whole-rock geochemistry suggests that the granite stages are genetically related and share similar petrogenetic histories. Weighted mean zircon 206Pb/238U dates from the older magmatic stage 1 alkali-feldspar quartz syenite and stage 2 alkali-feldspar granite are 1112.36 ± 0.35 and 1112.46 ± 0.37 Ma, respectively. The weighted mean ΔHf(t) values varying from +5.3 to +7.2 are similar to those of other regional ca. 1.1 Ga magmatic rocks throughout southwestern Laurentia. Geochemical characteristics, petrological modeling, and enriched Hf isotopic composition suggest fractional crystallization of a basaltic magma that was produced by melting of an enriched mantle reservoir. However, zircon inheritance ages of ca. 1.3 Ga and 1.26â1.15 Ga are consistent with a minor contribution from felsic crustal basement. Our data and regional geology are consistent with a post-collisional slab break-off that facilitated asthenospheric upwelling and partial melting of the enriched mantle, possibly subcontinental lithospheric mantle, extending from Llano Uplift, Texas, in the southeast to California to the northwest. Magma thus generated upon differentiation produced ferroan and A-type granitoids
A model of linear chain submonolayer structures. Application to Li/W(112) and Li/Mo(112)
We propose a lattice gas model to account for linear chain structures
adsorbed on (112) faces of W and Mo. The model includes a dipole-dipole
interaction as well as a long-ranged indirect interaction. We have explicitly
demonstrated that the periodic ground states depend on a competition between
dipole-dipole and indirect interaction. The effect of temperature is studied
within the molecular-field approximation. The numerical results show that for
dipole-dipole interaction only, all long periodic linear chain phases are
suppressed to low temperatures. However, when the long-range indirect
interaction becomes important, the long-periodic linear chain phases start to
fill up the phase diagram and develop a high thermal stability. Model
parameters are chosen to reconstruct a sequence of long-periodic phases as
observed experimentally for Li/Mo(112) and Li/W(112).Comment: RevTeX 9 pages + 5 Postscript figures (included), uses newdoc.sty
(included), to be published in Surface Scienc
Single parameter scaling in one-dimensional localization revisited
The variance of the Lyapunov exponent is calculated exactly in the
one-dimensional Anderson model with random site energies distributed according
to the Cauchy distribution. We find a new significant scaling parameter in the
system, and derive an exact analytical criterion for single parameter scaling
which differs from the commonly used condition of phase randomization. The
results obtained are applied to the Kronig-Penney model with the potential in
the form of periodically positioned -functions with random strength.Comment: Phys. Rev. Lett. 84, 2678 (2000
Failure of single-parameter scaling of wave functions in Anderson localization
We show how to use properties of the vectors which are iterated in the
transfer-matrix approach to Anderson localization, in order to generate the
statistical distribution of electronic wavefunction amplitudes at arbitary
distances from the origin of disordered systems. For
our approach is shown to reproduce exact diagonalization results
available in the literature. In , where strips of width sites
were used, attempted fits of gaussian (log-normal) forms to the wavefunction
amplitude distributions result in effective localization lengths growing with
distance, contrary to the prediction from single-parameter scaling theory. We
also show that the distributions possess a negative skewness , which is
invariant under the usual histogram-collapse rescaling, and whose absolute
value increases with distance. We find for the
range of parameters used in our study, .Comment: RevTeX 4, 6 pages, 4 eps figures. Phys. Rev. B (final version, to be
published
Decay Rate Distributions of Disordered Slabs and Application to Random Lasers
We compute the distribution of the decay rates (also referred to as residues)
of the eigenstates of a disordered slab from a numerical model. From the
results of the numerical simulations, we are able to find simple analytical
formulae that describe those results well. This is possible for samples both in
the diffusive and in the localised regime. As example of a possible
application, we investigate the lasing threshold of random lasers.Comment: 11 pages, 11 figure
Recommended from our members
Frailty in liver transplantation: An expert opinion statement from the American Society of Transplantation Liver and Intestinal Community of Practice
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149699/1/ajt15392_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149699/2/ajt15392.pd
Anderson-localization versus delocalization of interacting fermions in one dimension
Using the density matrix renormalization group algorithm, we investigate the
lattice model for spinless fermions in one dimension in the presence of a
strong interaction and disorder. The phase sensitivity of the ground state
energy is determined with high accuracy for systems up to a size of 60 lattice
constants. This quantity is found to be log-normally distributed. The
fluctuations grow algebraically with system size with a universal exponent of
~2/3 in the localized region of the phase diagram. Surprizingly, we find, for
an attractive interaction, a delocalized phase of finite extension. The
boundary of this delocalized phase is determined.Comment: 5 pages, 6 figures, revte
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