Random conformally invariant curves and quantum group techniques

Stochastic Analysis Seminar Series

In this talk we consider two questions about conformally invariant random curves known as Schramm-Loewner evolutions (SLE). The first question is about the "boundary zig-zags", i.e. the probabilities for a chordal SLE to pass through small neighbourhoods of given boundary points in a given order. The second question is that of obtaining explicit descriptions of "multiple SLE pure geometries", i.e. those extremal multiple SLE probability measures which cannot be expressed as non-trivial convex combinations of other multiple SLEs. For both problems one needs to find solutions of a system of partial differential equations with asymptotic conditions written recursively in terms of solution of the same problem with a smaller number of variables. We present a general correspondence, which translates these problems to linear systems of equations in finite dimensional representations of the quantum group U_q(sl_2), and we then explicitly solve these systems. The talk is based on joint works with Eveliina Peltola (Helsinki), and with Niko Jokela (Santiago de Compostela) and Matti Järvinen (Crete).

Location:
Speaker(s):

Kalle Kytola (Helsinki University of Technology)

Date:
Monday, May 13, 2013 - 15:45
to 16:45