Abstract: 

Simmons and Cardy recently predicted a formula for the   
probability that the chordal SLE$_{8/3}$ path passes to the left of   
two points in the upper half-plane. We discuss a rigorous proof of   
their formula. Starting from this result, we derive explicit   
expressions for several natural connectivity functions for SLE$_{8/3}$   
bubbles and, equivalently, Brownian bubbles, conditioned to be of   
macroscopic size. By passing to a limit with such a bubble we   
construct a certain (chordal) restriction measure and in this way   
obtain a proof of a formula for the probability that two given points   
are between two commuting SLE$_{8/3}$ paths. The one-point version of   
this result has been predicted by Gamsa and Cardy.