Iterated Brownian motion ad libitum is not the pseudo-arc
Confluentes Mathematici, Volume 13 (2021) no. 1, pp. 35-42.

The construction of a random continuum 𝒞 from independent two-sided Brownian motions as considered in [11] almost surely yields a non-degenerate indecomposable continuum. We show that 𝒞 is not-hereditarily indecomposable and, in particular, it is (unfortunately) not the pseudo-arc.

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DOI: 10.5802/cml.70
Classification: 54F15, 60J65
Keywords: continuum, iterated Brownian motions, pseudo-arc

Jérôme Casse 1; Nicolas Curien 2

1 CEREMADE, CNRS, UMR 7534, Université Paris-Dauphine, PSL University, 75016 Paris, France
2 Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405, Orsay, France Institut Universitaire de France
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Jérôme Casse; Nicolas Curien. Iterated Brownian motion ad libitum is not the pseudo-arc. Confluentes Mathematici, Volume 13 (2021) no. 1, pp. 35-42. doi : 10.5802/cml.70. https://cml.centre-mersenne.org/articles/10.5802/cml.70/

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