 Two-sided SLE boundary swallowing probability

ID: two-sided-sle-boundary-swallowing-probability

For

1 < d < 2

, couple Bessel flows

X > 0 > Y

with the same Brownian motion and let

v = x / y < 0

. Then

P (τ_{x} > τ_{y}) = \frac{\int _{v}^{0} \frac{d u}{( - u ) ^{d - 1} ( 1 - u ) ^{4 - 2 d}}}{\int _{- \infty}^{0} \frac{d u}{( - u ) ^{d - 1} ( 1 - u ) ^{4 - 2 d}}} .

It is the probability that the SLE hull swallows the chosen point on the negative side before the point on the positive side.

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