The Local Limit Theorem: A Historical Perspective

Spermatozoa: A Historical Perspective

The 100,000th scientific article on the subject of spermatozoa was recently published. Many studies have evaluated the characteristics of this important cell leading to great discoveries. Since its first observation and description in 1677, many important characteristics have been described regarding this highly fascinating gamete. In this review, our objective has been to provide a historical ...

The Local Central Limit Theorem for a Gibbs Random Field

We extend the validity of the implication of a local limit theorem from an integral one. Our extension eliminates the finite range assumption present in the previous works by using the cluster expansion to analyze the contribution from the tail of the potential. 1. Definitions and Results 1.1. Assumptions We consider a v-dimensional lattice spin system, to each χeZ is associated a spin sx that ...

A Local Limit Theorem for the Critical Random Graph

We consider the limit distribution of the orders of the k largest components in the Erdős-Rényi random graph inside the “critical window” for arbitrary k. We prove a local limit theorem for this joint distribution and derive an exact expression for the joint probability density function.

Description of the human races: A historical perspective

The Brauer-Hasse-Noether theorem in historical perspective

A Multivariate Central Limit Theorem for Continuous Local Martingales

A theorem on the weak convergence of a properly normalized multivariate continuous local martingale is proved. The time-change theorem used for this purpose allows for short and transparent arguments. 1991 Mathematics Subject Classification: 60F05, 60G44