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2010

Some remarks on SLE bubbles and Schramm's two-point observable

Beliaev, Dmitry, Viklund, Fredrik Johansson

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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.

In this paper we give a rigorous proof of their formula.
Starting from this result, we derive explicit expressions for several natural connectivity functions for SLE(8/3) 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.

Some remarks on SLE bubbles and Schramm's two-point observable · Around

Built on

A percolation formula
O. Schramm · 2001
Earlier work this paper cites.
Conformal restriction: The chordal case
G. F. Lawler, O. Schramm, and W. Werner · 2003
Earlier work this paper cites.
Brownian beads
B. Virág · 2003
Earlier work this paper cites.
On the scaling limit of planar self-avoiding walk
G. F. Lawler, O. Schramm, and W. Werner · 2004
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