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arXiv · 1801.03741

Double asymptotic for random walks on hypercubes

Fabien Montégut
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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.

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Fabien Montégut. 2018-01-11. Double asymptotic for random walks on hypercubes. https://arxiv.org/abs/1801.03741

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