Jonathan Tsai, CUHK,
Conformally
Invariant Random Curves on Riemann Surfaces Satisfying the Restriction
Property Abstract Let be a family of
random curves such that for each planar domain D with a and
b on the boundary, is a random
curve in D from a to b. We say that the family of curves S satisfies the restriction property if for any compact set K in D avoiding a and b, conditioned to
avoid K is just . Lawler, Schramm and Werner discovered a way of
constructing the family of curves S
when D is a simply-connected domain.
In particular, it is Stochastic Loewner evolution
with parameter 8/3. In this talk, we will
outline an extension of this construction to non-simply connected finite
Riemann surfaces with boundary. From this, we can deduce some asymptotic
properties of the family of curves S. |