Abstract
It is shown that the trace of three dimensional Brownian motion contains arithmetic progressions of length 5 and no arithmetic progressions of length 6 a.s.
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References
P. Mörters, Y. Peres, Brownian Motion. Cambridge Series in Statistical and Probabilistic Mathematics, vol. 30. (Cambridge University Press, Cambridge, 2010), pp. xii+ 403
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Benjamini, I., Kozma, G. (2020). Arithmetic Progressions in the Trace of Brownian Motion in Space. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2256. Springer, Cham. https://doi.org/10.1007/978-3-030-36020-7_4
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DOI: https://doi.org/10.1007/978-3-030-36020-7_4
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