Convergence rate to a lower tail dependence coefficient of a skew-t distribution

We examine the rate of decay to the limit of the tail dependence coefficient of a bivariate skew t distribution which always displays asymptotic tail dependence. It contains as a special case the usual bivariate symmetric t distribution, and hence is an appropriate (skew) extension. The rate is asymptotically power-law. The second-order structure of the univariate quantile function for such a skew-t distribution is a central issue.Comment: 14 page

Explicit forms for ergodicity coefficients of stochastic matrices

AbstractMotivated by explicit expressions appearing in the work of A. Rhodius (1993) for n×n stochastic matrices P, it is shown that ordinary matrix norms on Rn−1 for (n−1)×(n−1) matrices of the form APB can be used to generate results of this kind

Normed-convergence theory for supercritical branching processes

AbstractA proof is given of the basic normed-convergence theorem for the ordinary supercritical Bienaymé-Galton-Watson process with finite mean. Part of it is adapted to obtain an analogous result for inhomogeneous supercritical processes (i.e. branching processes in varying environment). This is used in part to give a detailed discussion on the normed- convergence behaviour of the ordinary process in the ‘explosive’ case (i.e with infinite mean); and rather pathological limit behaviour is found to obtain

Approaching the Ground State of a Quantum Spin Glass using a Zero-Temperature Quantum Monte Carlo

Here we discuss the annealing behavior of an infinite-range $\pm J$ Ising spin glass in presence of a transverse field using a zero-temperature quantum Monte Carlo. Within the simulation scheme, we demonstrate that quantum annealing not only helps finding the ground state of a classical spin glass, but can also help simulating the ground state of a quantum spin glass, in particularly, when the transverse field is low, much more efficiently.Comment: 8 pages, 6 fig

Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure

For directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known