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Title:
Two-point Schramm’s Formula and SLE-8/3 Bubbles
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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.
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