Conformal welding is a way of gluing Riemann surfaces along their boundary; however, the existence and uniqueness of the resulting object is in general difficult to determine; this is the conformal welding problem.
We prove that a natural conformal welding problem associated to the continuum random tree (CRT) has a (unique) solution, giving rise to a `canonical’ random embedding of the CRT in the plane.
Joint work with Steffen Rohde.
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