2,857 research outputs found
Next-to-next-to-leading-order epsilon expansion for a Fermi gas at infinite scattering length
We extend previous work on applying the epsilon-expansion to universal
properties of a cold, dilute Fermi gas in the unitary regime of infinite
scattering length. We compute the ratio xi = mu/epsilon_F of chemical potential
to ideal gas Fermi energy to next-to-next-to-leading order (NNLO) in
epsilon=4-d, where d is the number of spatial dimensions. We also explore the
nature of corrections from the order after NNLO.Comment: 28 pages, 14 figure
Stability of 3D Cubic Fixed Point in Two-Coupling-Constant \phi^4-Theory
For an anisotropic euclidean -theory with two interactions [u
(\sum_{i=1^M {\phi}_i^2)^2+v \sum_{i=1}^M \phi_i^4] the -functions are
calculated from five-loop perturbation expansions in
dimensions, using the knowledge of the large-order behavior and Borel
transformations. For , an infrared stable cubic fixed point for
is found, implying that the critical exponents in the magnetic phase
transition of real crystals are of the cubic universality class. There were
previous indications of the stability based either on lower-loop expansions or
on less reliable Pad\'{e approximations, but only the evidence presented in
this work seems to be sufficently convincing to draw this conclusion.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at
http://www.physik.fu-berlin.de/~kleinert/kleiner_re250/preprint.htm
Statistics of extremes under random censoring
We investigate the estimation of the extreme value index when the data are
subject to random censorship. We prove, in a unified way, detailed asymptotic
normality results for various estimators of the extreme value index and use
these estimators as the main building block for estimators of extreme
quantiles. We illustrate the quality of these methods by a small simulation
study and apply the estimators to medical data.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ104 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Projection Estimates of Constrained Functional Parameters
AMS classifications: 62G05; 62G07; 62G08; 62G20; 62G32;estimation;convex function;extreme value copula;Pickands dependence function;projection;shape constraint;support function;tangent cone
Obtaining Bounds on The Sum of Divergent Series in Physics
Under certain circumstances, some of which are made explicit here, one can
deduce bounds on the full sum of a perturbation series of a physical quantity
by using a variational Borel map on the partial series. The method is
illustrated by applying it to various examples, physical and mathematical.Comment: 33 pages, Journal Versio
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