Boostrap Random Walk

Consider the increments {ξ_k}_k of a simple symmetric random walk X. Denote by η_n = ξ₁⋯ξ_n and consider the random walk Y having increments {η_k}_k. The random walks X and Y are strongly dependent. Still the 2-dimensional walk (X,Y), properly rescaled, converges to a two dimensional Brownian motion. The goal of this talk is to present the proof of this fact and discuss its generalizations.

 

 

Professor Collevecchio is a Senior Lecturer at Monash University, Australia. He received his PhD from the Purdue University, after which he has been a post-doc at the University of Chieti and at the Max Planck Institute in Lepzig, and Assistant Professor at the University of Venice. His research areas include interacting processes, large deviations, random graphs, and study of mixing times for markov chains.