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Conformal restriction: the trichordal case

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If you have a question about this talk, please contact Perla Sousi.

In the present talk, we focus on the study of random subsets of a given simply connected domain that join three marked boundary points (namely ’the trichordal case’) and that satisfy the additional restriction property. The study of such properties in two-dimensions was initiated by Lawler, Schramm and Werner who focused on the chordal case.

The construction of this family of random sets relies on special variants of SLE8 /3 processes with a drift term in the driving function that involves hypergeometric functions. It turns out that such a random set can not be a simple curve simultaneously in the neighborhood of all three marked points, and that the exponent = 20/27 shows up in the description of the law of the skinniest possible symmetric random set with this trichordal restriction property.

This talk is part of the Probability series.

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