Title: Scaling limits of random curves using discrete complex analysis and martingales
Speaker: Antti Kemppainen
University of Helsinki
Time: Monday 22 November 2010, 16:15-18:00
Place: Room U322
TKK Main Building (Otakaari 1 M, Espoo)
Abstact:
I will describe recent progress in the understanding of structure of random
interfaces in lattice models of statistical physics. In 2D, the interfaces are
random curves. One of the reasons why the critical point of the model is
interesting is that the fluctuations in these curves are in the macroscopic
scale and therefore the natural scaling limit is nontrivial. The set of possible
continuum limits of the interfaces at criticality is known by the seminal work
of Oded Schramm, who showed that conformal invariance and the domain Markov
property, which are properties expected from the physics, characterize a family
of random curves which are nowadays known as Schramm-Loewner evolutions (SLE).
Especially, I will describe how discrete complex analysis and martingales are
used in showing the connection between the discrete interfaces and SLE.