We show that the central limit theorem for linear statistics over determinantal point processes with J-Hermitian kernels holds under fairly general conditions. In particular, we establish Gaussian on union of two copies ℝd when correlation are translation-invariant.

L et us apply our newly acquired tools to the fundamental diagnostics in dynamics: Is a given system ‘chaotic’? And if so, how chaotic? If all points in example 2.3 a neighborhood of a trajectory converge toward the same orbit, the attractor is a fixed point or a limit cycle. However, if the attractor is strange, any two section 1.3.1 trajectories x(t) = f (x0) and x(t)+δx(t) = f (x0 + δx0) tha...

An aspatial version for the famous Schelling’s segregation model has recently been proposed, which, called two-room model, is still in an agent-based format like the original Schelling model. In the present study, we propose a new, state equation version of the Schelling model. The new equation is based on the two-room model and is derived in terms of a set of discrete maps. Fixed point solutio...

This talk is focused on such systems in overload. We look at a single queue and consider the scenario where customers leave impatient as their waiting time grows too large. We propose a fluid (functional LLN) approximation of this system and investigate the fixed point of this approximation. This leads to several qualitative insights into the dynamics of PS models with impatience. We show that ...

In this paper, the existence of 12 small limit cycles is proved for cubic order Z2-equivariant vector fields, which bifurcate from fine focus points. This is a new result in the study of the second part of the 16th Hilbert problem. The system under consideration has a saddle point, or a node, or a focus point (including center) at the origin, and two weak focus points which are symmetric about ...