  The study of conformal restriction properties in two-dimensions has been
initiated by Lawler, Schramm and Werner who focused on the natural and
important chordal case: They characterized and constructed all random subsets
of a given simply connected domain that join two marked boundary points and
that satisfy the additional restriction property. The radial case (sets joining
an inside point to a boundary point) has then been investigated by Wu. In the
present paper, we study the third natural instance of such restriction
properties, namely the "trichordal case", where one looks at random sets that
join three marked boundary points. This case involves somewhat more
technicalities than the other two, as the construction of this family of random
sets relies on special variants of SLE$_{8/3}$ 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 $\alpha = 20/27$ shows up in
the description of the law of the skinniest possible symmetric random set with
this trichordal restriction property.
