Local Central Limit Theorem for a Random Walk Perturbed in One Point

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 limit theorem for perturbed random walks

The main result reported here is a Stone type local limit theorem for perturbed random walks 2, = S, + 5, when some slow variation conditions are imposed on 5,‘s.

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.

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 ...

Central and Local Limit Theories in Markov Dependent Random Variables