 Home

Codex Wiki

Mathematics

Area of mathematics

Probability and statistics

Probability theory

Stochastic process

Schramm–Loewner evolution

Boundary-point Bessel flow for SLE

{c}

For $1<d<2$, couple Bessel flows $X>0>Y$ with the same Brownian motion and let $v=x/y<0$. Then
$$
\mathbb P(\tau_x>\tau_y)=\frac{\displaystyle\int_v^0\frac{du}{(-u)^{d-1}(1-u)^{4-2d}}}{\displaystyle\int_{-\infty}^0\frac{du}{(-u)^{d-1}(1-u)^{4-2d}}}.
$$
It is the probability that the SLE hull swallows the chosen point on the negative side before the point on the positive side.

Two-sided SLE boundary swallowing probability

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 203 / 3 / d / Solution

Two-sided SLE boundary swallowing probability

 Ancestors (8)

 Incoming links (1)

 Discussion (0)

 Articles by others on the same topic (0)

Two-sided SLE boundary swallowing probability

 Ancestors (8)

 Incoming links (1)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)