Double asymptotic for random walks on hypercubes

2018/01/11 by Montégut, Fabien
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1801.03741

Abstract

We consider the sum of the coordinates of a simple random walk on the K-dimensional hypercube, and prove a double asymptotic of this process, as both the time parameter n and the space parameter K tend to infinity. Depending on the asymptotic ratio of the two parameters, they converge towards either a Brownian motion, an Ornstein-Uhlenbeck process or an i.i.d. collection of Gaussian variables.

Related

• Stopping Times of Random Walks on a Hypercube
• Limit theorems for projections of random walk on a hypersphere
• A non-local Random Walk on the Hypercube
• A note on random walks in a hypercube
• Extremal points of high dimensional random walks and mixing times of a Brownian motion on the sphere