We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number of extracted balls of a certain color given the past is assumed to be hypergeometric. We prove some central limit theorems in the sense of stable convergence ...

The dynamics of an ensemble of identically prepared two-qubit systems is investigated which is subjected to the iteratively applied measurements and conditional selection of a typical entanglement purification protocol. The resulting dynamics exhibits strong sensitivity to initial conditions. For one class of initial states two types of islands characterize the asymptotic limit. They correspond...

Ecologists have recently used integral projection models (IPMs) to study fish and other animals which continue grow throughout their lives. Such cannot shrink, since they bony skeletons; a mathematical consequence of this is that the kernel operator T unbounded, not compact. To our knowledge, all theoretical work done on IPMs has assumed compact, in particular bounded kernel. A priori, it uncle...

‎Recently a first-order Spatial Integer-valued Autoregressive‎ ‎SINAR(1,1) model was introduced to model spatial data that comes‎ ‎in counts citep{ghodsi2012}‎. ‎Some properties of this model‎ ‎have been established and the Yule-Walker estimator has been‎ ‎proposed for this model‎. ‎In this paper‎, ‎we introduce the...

We study the conformal window of asymptotically free gauge theories containing ${N}_{f}$ flavors fermion matter transforming to vector and two-index representations $SO(N),SU(N)$ $Sp(2N)$ groups. For $SO(N)$ we also consider spinorial representation. determine critical number ${N}_{f}^{\mathrm{cr}}$, corresponding lower end window, by using conjectured condition on anomalous dimension bilinear ...

We introduce the affine ensemble, a class of determinantal point processes (DPP) in half-plane $\mathbb{C}^{+}$ associated with $ax + b$ (affine) group, depending on an admissible Hardy function $\psi$. obtain asymptotic behavior variance, exact value constant, and non-asymptotic upper lower bounds for variance compact set $\Omega \subset \mathbb{C}^{+}$. As special case one recovers DPP relate...