Iterated Brownian motion ad libitum is not the pseudo-arc

Jérôme Casse (1) , Nicolas Curien (1)

1 Université Paris-Saclay

We show that the construction of a random continuum $\mathcal{C}$ from independent two-sided Brownian motions as considered in arXiv:2004.01367 almost surely yields a non-degenerate indecomposable but not-hereditary indecomposable continuum. In particular $\mathcal{C}$ is (unfortunately) not the pseudo-arc.

Domaines: Mathématiques [math]

Jérôme Casse, Nicolas Curien. Iterated Brownian motion ad libitum is not the pseudo-arc. 2021. ⟨hal-03287260⟩