A local limit theorem and loss of rotational symmetry of planar symmetric simple random walk

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.

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...

Scaling limit of simple random walk on supercritical percolation clusters

Central Limit Theorem for the Excited Random Walk in Dimension

We prove that a law of large numbers and a central limit theorem hold for the excited random walk model in every dimension d ≥ 2.

A Local Limit Theorem for Sums of Independent Random Vectors

We prove a local limit theorem for sums of independent random vectors satisfying appropriate tightness assumptions. In particular, the local limit theorem holds in dimension 1 if the summands are uniformly bounded.