Double asymptotic for random walks on hypercubes
Probability
2019-09-23 v2
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.
Cite
@article{arxiv.1801.03741,
title = {Double asymptotic for random walks on hypercubes},
author = {Fabien Montégut},
journal= {arXiv preprint arXiv:1801.03741},
year = {2019}
}
Comments
Journal of Theoretical Probability, Springer, In press