Double Asymptotic for Random Walks on Hypercubes

Fabien Montégut ()
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Fabien Montégut: Université de Toulouse CNRS

Journal of Theoretical Probability, 2019, vol. 32, issue 4, 2044-2065

Abstract: 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, the rescaled processes converge toward either a “stationary Brownian motion,” an Ornstein–Uhlenbeck process or a Gaussian white noise.

Keywords: Limit theorems; Markov chains; Hypercube; 60F17; 60J10 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-019-00931-y

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