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Beskrivelse
A long open problem in probability theory has been the following: Can the graph of planar Brownian motion be split by a straight line? Let $Z_t$ be two-dimensional Brownian motion. Say that a straight line $\mathcal L$ is a cut line if there exists a time $t \in (0,1)$ such that the trace of $\{ Z_s: 0 \leq s < t\}$ lies on one side of $\mathcal L$ and the trace of $\{Z_s: t < s < 1\}$ lies on the other side of $\mathcal L$. In this volume, the authors provide a solution, discuss related works, and present a number of open problems.