Regularly varying correlation functions and KMO-Langevin equations

Regularly Varying Solutions of Generalized Thomas-fermi Equations

An Extension of the Class of Regularly Varying Functions

We define a new class of positive and Lebesgue measurable functions in termsof their asymptotic behavior, which includes the class of regularly varying functions.We also characterize it by transformations, corresponding to generalized momentswhen these functions are random variables. We study the properties of this new classand discuss their applications to Extreme Value The...

Regularly varying probability densities

The convolution of regularly varying probability densities is proved asymptotic to their sum, and hence is also regularly varying. Extensions to rapid variation, O-regular variation, and other types of asymptotic decay are also given. Regularly varying distribution functions have long been used in probability theory; see e.g. Feller [7, VIII.8], Bingham, Goldie and Teugels [5, Ch. 8]. This note...

Regularly Varying Solutions of Perturbed Euler Differential Equations and Related Functional Differential Equations

An asymptotic analysis in the framework of Karamata regularly varying functions is performed for the solutions of second order linear differential and functional differential equations in the critical case i.e., when condition (1.5) as given below, holds.

Ising Chain in Regularly Alternating Transverse Field: Spin Correlation Functions

We consider the spin1 2 Ising chain in a regularly alternating transverse field to examine the effects of regular alternation on the quantum phase transition inherent in the quantum Ising chain. The number of quantum phase transition points strongly depends on the specific set of the Hamiltonian parameters but never exceeds 2p where p is the period of alternation. Calculating the spin correlati...