# Percolation on the hyperbolic plane and convergence to SLE(6) on hyperbolic plane

In "Percolation in the hyperbolic plane" the authors study the properties of percolation in the hyperbolic plane. Smirnov and others proved convergence of isotropic percolation to SLE(6).

Do these results follow for the hyperbolic case too?

Findings:

1)L. Arosio, F. Bracci, "Infinitesimal generators and the Loewner equation on complete hyperbolic manifolds,"

So there is a natural candidate.

thanks

Smirnov's theorem assert the convergence to SLE in the scaling limit: one discretizes the domain with the triangular lattice of mesh size $\delta$, and lets $\delta$ go to zero. It is only proven for the triangular lattice; it's a major open problem to prove universality of this result (in fact, even to extend it to the square lattice).