Presented by:
Joonas Turunen
Date:
Friday 13th July 2018 - 09:35 to 09:55
Venue:
INI Seminar Room 1
Event:
Abstract:
In this talk, I consider
Boltzmann random triangulations coupled to the Ising model on their faces,
under Dobrushin boundary conditions and at the critical point. First, the
partition function is computed and the perimeter exponent shown to be 7/3 instead
of the exponent 5/2 for
uniform triangulations. Then, I sketch the construction of the local
limit in distribution when the two components of the Dobrushin boundary tend to
infinity one after the other, using the peeling process along an Ising interface.
In particular, the main interface in the local limit touches the
(infinite) boundary almost surely only finitely many times, a behavior opposite
to that of the Bernoulli percolation on uniform maps. Some scaling limits
closely related to the perimeters of clusters are also discussed. This is based
on a joint work with Linxiao Chen.
