9,589 research outputs found
Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Cases of Large and Critical Dimensions
Functional central limit theorem; Occupation time fluctuation; Branching particle system; Generalized Wiener process; Critical dimension
Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Case of Long-Range Dependence
Functional central limit theorem; Occupation time
uctuation; Branching particle system; Distribution-valued Gaussian process; Fractional Brownian motion; Sub-fractional Brownian motion; Long-range dependence
A Long Range Dependence Stable Process and an Infinite Variance Branching System
We prove a functional limit theorem for the rescaled occupation time fluctuations of a (d, , )- branching particle system (particles moving in Rd according to a symmetric -stable L´evy process, branching law in the domain of attraction of a (1 + )-stable law, 0 d/(d + ), which coincides with the case of finite variance branching ( = 1), and another one for d/(d + ), where the long range dependence depends on the value of . The long range dependence is characterized by a dependence exponent which describes the asymptotic behavior of the codierence of increments of on intervals far apart, and which is d/ for the first case and (1 + - d/(d + ))d/ for the second one. The convergence proofs use techniques of S0(Rd)-valued processes.Branching particle system, occupation time fluctuation, functional limit theorem, stable process, long range dependence.
Occupation Time Fluctuations of an Infinite Variance Branching System in Large Dimensions
We prove limit theorems for rescaled occupation time fluctuations of a (d, , )-branching particle system (particles moving in Rd according to a spherically symmetric -stable L´evy process, (1 + )- branching, 0 (1 + )/. The fluctuation processes are continuous but their limits are stable processes with independent increments, which have jumps. The convergence is in the sense of finite-dimensional distributions, and also of space-time random fields (tightness does not hold in the usual Skorohod topology). The results are in sharp contrast with those for intermediate dimensions, /Branching particle system, critical and large dimensions, limit theorem, occupation time fluctuation, stable process.
Thiemann transform for gravity with matter fields
The generalised Wick transform discovered by Thiemann provides a
well-established relation between the Euclidean and Lorentzian theories of
general relativity. We extend this Thiemann transform to the Ashtekar
formulation for gravity coupled with spin-1/2 fermions, a non-Abelian
Yang-Mills field, and a scalar field. It is proved that, on functions of the
gravitational and matter phase space variables, the Thiemann transform is
equivalent to the composition of an inverse Wick rotation and a constant
complex scale transformation of all fields. This result holds as well for
functions that depend on the shift vector, the lapse function, and the Lagrange
multipliers of the Yang-Mills and gravitational Gauss constraints, provided
that the Wick rotation is implemented by means of an analytic continuation of
the lapse. In this way, the Thiemann transform is furnished with a geometric
interpretation. Finally, we confirm the expectation that the generator of the
Thiemann transform can be determined just from the spin of the fields and give
a simple explanation for this fact.Comment: LaTeX 2.09, 14 pages, no figure
Inner boundary conditions for black hole Initial Data derived from Isolated Horizons
We present a set of boundary conditions for solving the elliptic equations in
the Initial Data Problem for space-times containing a black hole, together with
a number of constraints to be satisfied by the otherwise freely specifiable
standard parameters of the Conformal Thin Sandwich formulation. These
conditions altogether are sufficient for the construction of a horizon that is
instantaneously in equilibrium in the sense of the Isolated Horizons formalism.
We then investigate the application of these conditions to the Initial Data
Problem of binary black holes and discuss the relation of our analysis with
other proposals that exist in the literature.Comment: 13 pages. Major general revision. Section V comparing with previous
approaches restructured; discussion on the lapse boundary condition extended.
Appendix with some technical details added. Version accepted for publication
in Phys.Rev.
Hunting long-lived gluinos at the Pierre Auger Observatory
Eventual signals of split sypersymmetry in cosmic ray physics are analyzed in
detail. The study focusses particularly on quasi-stable colorless R-hadrons
originating through confinement of long-lived gluinos (with quarks,
anti-quarks, and gluons) produced in pp collisions at astrophysical sources.
Because of parton density requirements, the gluino has a momentum which is
considerable smaller than the energy of the primary proton, and so production
of heavy (mass ~ 500 GeV) R-hadrons requires powerful cosmic ray engines able
to accelerate particles up to extreme energies, somewhat above 10^{13.6} GeV.
Using a realistic Monte Carlo simulation with the AIRES engine, we study the
main characteristics of the air showers triggered when one of these exotic
hadrons impinges on a stationary nucleon of the Earth atmosphere. We show that
R-hadron air showers present clear differences with respect to those initiated
by standard particles. We use this shower characteristics to construct
observables which may be used to distinguish long-lived gluinos at the Pierre
Auger Observatory.Comment: 13 pages revtex, 9 eps figures. A ps version with high resolution
figures is available at
http://www.hep.physics.neu.edu/staff/doqui/rhadron_highres.p
Active Galactic Nuclei with Candidate Intermediate-Mass Black Holes
We present an initial sample of 19 intermediate-mass black hole candidates in
active galactic nuclei culled from the First Data Release of the Sloan Digital
Sky Survey. Using the linewidth-luminosity-mass scaling relation established
for broad-line active nuclei, we estimate black hole masses in the range of 8 x
10^4 - 10^6 solar masses, a regime in which only two objects are currently
known. The absolute magnitudes are faint for active galactic nuclei, ranging
from M_g of -15 to -18 mag, while the bolometric luminosities are all close to
the Eddington limit. The entire sample formally satisfies the linewidth
criterion for so-called narrow-line Seyfert 1 galaxies; however, they display a
wider range of FeII and [OIII] (5007) line strengths than is typically observed
in this class of objects. Although the available imaging data are of
insufficient quality to ascertain the detailed morphologies of the host
galaxies, it is likely that the majority of the hosts are relatively late-type
systems. The host galaxies have estimated g-band luminosities ~ 1 mag fainter
than M* for the general galaxy population at z of 0.1. Beyond simply extending
the known mass range of central black holes in galactic nuclei, these objects
provide unique observational constraints on the progenitors of supermassive
black holes. They are also expected to contribute significantly to the
integrated signal for future gravitational wave experiments.Comment: ApJ Accepted, 13 pages, 9 figures, uses emulateapj.cl
Predictions for the Cosmogenic Neutrino Flux in Light of New Data from the Pierre Auger Observatory
The Pierre Auger Observatory (PAO) has measured the spectrum and composition
of the ultrahigh energy cosmic rays with unprecedented precision. We use these
measurements to constrain their spectrum and composition as injected from their
sources and, in turn, use these results to estimate the spectrum of cosmogenic
neutrinos generated in their propagation through intergalactic space. We find
that the PAO measurements can be well fit if the injected cosmic rays consist
entirely of nuclei with masses in the intermediate (C, N, O) to heavy (Fe, Si)
range. A mixture of protons and heavier species is also acceptable but (on the
basis of existing hadronic interaction models) injection of pure light nuclei
(p, He) results in unacceptable fits to the new elongation rate data. The
expected spectrum of cosmogenic neutrinos can vary considerably, depending on
the precise spectrum and chemical composition injected from the cosmic ray
sources. In the models where heavy nuclei dominate the cosmic ray spectrum and
few dissociated protons exceed GZK energies, the cosmogenic neutrino flux can
be suppressed by up to two orders of magnitude relative to the all-proton
prediction, making its detection beyond the reach of current and planned
neutrino telescopes. Other models consistent with the data, however, are
proton-dominated with only a small (1-10%) admixture of heavy nuclei and
predict an associated cosmogenic flux within the reach of upcoming experiments.
Thus a detection or non-detection of cosmogenic neutrinos can assist in
discriminating between these possibilities.Comment: 10 pages, 7 figure
Reality conditions for Ashtekar variables as Dirac constraints
We show that the reality conditions to be imposed on Ashtekar variables to
recover real gravity can be implemented as second class constraints a la Dirac.
Thus, counting gravitational degrees of freedom follows accordingly. Some
constraints of the real theory turn out to be non-polynomial, regardless of the
form, polynomial or non-polynomial, taken for the reality conditions. We
comment upon the compatibility of our approach with the recently proposed Wick
transform point of view, as well as on some alternatives for dealing with such
second class constraints.Comment: 16 pages, plain LaTeX, submitted to Class. Quant. Grav. E-mail:
[email protected]
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