A Local Limit Theorem for the Critical Random Graph

Central and Local Limit Theories in Markov Dependent Random Variables

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...

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

A local central limit theorem for triangles in a random graph

In this paper, we prove a local limit theorem for the distribution of the number of triangles in the Erdos-Renyi random graph G(n, p), where p ∈ (0, 1) is a fixed constant. Our proof is based on bounding the characteristic function ψ(t) of the number of triangles, and uses several different conditioning arguments for handling different ranges of t.

A ug 2 01 1 Local central limit theorems in stochastic geometry Mathew

We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply this result to various quantities arising in stochastic geometry, including: size of the largest component for percolation on a box; number of components, numbe...