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 $\phi^4$-theory with two interactions [u (\sum_{i=1^M {\phi}_i^2)^2+v \sum_{i=1}^M \phi_i^4] the $\beta$-functions are calculated from five-loop perturbation expansions in $d=4-\varepsilon$ dimensions, using the knowledge of the large-order behavior and Borel transformations. For $\varepsilon=1$, an infrared stable cubic fixed point for $M \geq 3$ 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