And/or trees: A local limit point of view

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

Fuzzy sets form A meta-system-theoretic point of view

Local Central Limit Theorem for Determinantal Point Processes

We prove a local central limit theorem (LCLT) for the number of points N(J) in a region J in Rd specified by a determinantal point process with an Hermitian kernel. The only assumption is that the variance of N(J) tends to infinity as |J | → ∞. This extends a previous result giving a weaker central limit theorem (CLT) for these systems. Our result relies on the fact that the Lee-Yang zeros of t...

The close limit from a null point of view : the advanced solution

We present a characteristic algorithm for computing the perturbation of a Schwarzschild spacetime by means of solving the Teukolsky equation. We implement the algorithm as a characteristic evolution code and apply it to compute the advanced solution to a black hole collision in the close approximation. The code successfully tracks the initial burst and quasinormal decay of a black hole perturba...

Close limit from a null point of view: The advanced solution

We present a characteristic algorithm for computing the perturbation of a Schwarzschild spacetime by means of solving the Teukolsky equation. We implement the algorithm as a characteristic evolution code and apply it to compute the advanced solution to a black hole collision in the close approximation. The code successfully tracks the initial burst and quasinormal decay of a black hole perturba...