On the shape of the connected components of the complement of
two-dimensional Brownian random interlacementsArticle
Authors: Orphée Collin ; Serguei Popov
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Orphée Collin;Serguei Popov
We study the limiting shape of the connected components of the vacant set of
two-dimensional Brownian random interlacements: we prove that the connected
component around $x$ is close in distribution to a rescaled \emph{Brownian
amoeba} in the regime when the distance from $x\in\mathbb{C}$ to the closest
trajectory is small (which, in particular, includes the cases $x\to\infty$ with
fixed intensity parameter $\alpha$, and $\alpha\to\infty$ with fixed $x$). We
also obtain a new family of martingales built on the conditioned Brownian
motion, which may be of independent interest.