25 research outputs found
Comparison of metrics obtained with analytic perturbation theory and a numerical code
We compare metrics obtained through analytic perturbation theory with their
numerical counterparts. The analytic solutions are computed with the CMMR
post-Minkowskian and slow rotation approximation due to Cabezas et al. (2007)
for an asymptotically flat stationary spacetime containing a rotating perfect
fluid compact source. The same spacetime is studied with the AKM numerical
multi-domain spectral code (Ansorg et al., 2002,2003). We then study their
differences inside the source, near the infinity and in the matching surface,
or equivalently, the global character of the analytic perturbation scheme.Comment: 4 pages, 2 figures and 1 table. To appear in the proceedings of the
2011 Spanish Relativity Meeting ERE201
Extreme value distributions and Renormalization Group
In the classical theorems of extreme value theory the limits of suitably
rescaled maxima of sequences of independent, identically distributed random
variables are studied. So far, only affine rescalings have been considered. We
show, however, that more general rescalings are natural and lead to new limit
distributions, apart from the Gumbel, Weibull, and Fr\'echet families. The
problem is approached using the language of Renormalization Group
transformations in the space of probability densities. The limit distributions
are fixed points of the transformation and the study of the differential around
them allows a local analysis of the domains of attraction and the computation
of finite-size corrections.Comment: 16 pages, 5 figures. Final versio
Generalized Central Limit Theorem and Renormalization Group
We introduce a simple instance of the renormalization group transformation in
the Banach space of probability densities. By changing the scaling of the
renormalized variables we obtain, as fixed points of the transformation, the
L\'evy strictly stable laws. We also investigate the behavior of the
transformation around these fixed points and the domain of attraction for
different values of the scaling parameter. The physical interest of a
renormalization group approach to the generalized central limit theorem is
discussed.Comment: 16 pages, to appear in J. Stat. Phy
Renormalization flow for extreme value statistics of random variables raised to a varying power
Using a renormalization approach, we study the asymptotic limit distribution
of the maximum value in a set of independent and identically distributed random
variables raised to a power q(n) that varies monotonically with the sample size
n. Under these conditions, a non-standard class of max-stable limit
distributions, which mirror the classical ones, emerges. Furthermore a
transition mechanism between the classical and the non-standard limit
distributions is brought to light. If q(n) grows slower than a characteristic
function q*(n), the standard limit distributions are recovered, while if q(n)
behaves asymptotically as k.q*(n), non-standard limit distributions emerge.Comment: 21 pages, 1 figure,final version, to appear in Journal of Physics
An approximate global stationary metric with axial symmetry for a perfect fluid with equation of state
A new analitycally approximated interior metric for a stationary compact perfect fluid with
equation of state µ+(1–n)p = µ0 is presented. Also, it is concluded that an object of this kind
can be a source of Wahlquist's metric
An approximate global stationary metric with axial symmetry for a perfect fluid with equation of state
We construct an approximate asymptotically flat stationary and axisymmetric vacuum metric by imposing matching conditions on an interior metric associated to a perfect fluid with equation of state µ+(1–n)p = µ0. A comparison between this vacuum metric and the Kerr one is made. Finally, a brief reflexion about the Wahlquist metric is commented in relation with our results