Polychromatic Arm Exponents for the Critical Planar FK-Ising model

Understand

Schramm Loewner Evolution (SLE) is a one-parameter family of random planar curves introduced by Oded Schramm in 1999 as the candidates for the scaling limits of the interfaces in the planar critical lattice models.

• This is the only possible process with conformal invariance and a certain "domain Markov property".
• In 2010, Chelkak and Smirnov proved the conformal invariance of the scaling limits of the critial planar FK-Ising model which gave the convergence of the interface to SLE$_{16/3}$.
• We derive the arm exponents of SLE$_{\kappa}$ for $\kappa\in (4,8)$.