Convergence of Ising interfaces to Schramm's SLE curves

Abstract

We show how to combine our earlier results to deduce strong convergence of the interfaces in the planar critical Ising model and its random-cluster representation to Schramm's SLE curves with parameter $\kappa =3$ and $\kappa =16/3$ respectively.

7 pages

References in corpus (1)

• The energy density in the planar Ising model

Cited by in corpus (6)

• Recent advances in percolation theory and its applications
• CLE percolations
• Crossing probabilities in topological rectangles for the critical planar FK-Ising model
• Schramm's formula for multiple loop-erased random walks
• Schramm--Loewner-evolution-type growth processes corresponding to Wess--Zumino--Witten theories
• Brownian Loops and Conformal Fields