Abstract
We present a simple model of a random walk with partial memory, which we call the random memory walk. We introduce this model motivated by the belief that it mimics the behavior of the once-reinforced random walk in high dimensions and with small reinforcement. We establish the transience of the random memory walk in dimensions three and higher, and show that its scaling limit is a Brownian motion.
To the memory of Vladas Sidoravicius
The author “Alexandre Stauffer” was supported by EPSRC Fellowship EP/N004566/1.
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Fribergh, A., Kious, D., Sidoravicius, V., Stauffer, A. (2021). Random Memory Walk. In: Vares, M.E., Fernández, R., Fontes, L.R., Newman, C.M. (eds) In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius. Progress in Probability, vol 77. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-60754-8_20
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DOI: https://doi.org/10.1007/978-3-030-60754-8_20
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