The paper proves, via conformal invariance of Brownian motion, that the hyperbolic secant law is invariant under g(x)=(2/π)log|sinh(πx/2)|, and gives a general transfer principle for exit distributions of symmetric domains.
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A note on invariance of the Cauchy and related distributions
The paper proves, via conformal invariance of Brownian motion, that the hyperbolic secant law is invariant under g(x)=(2/π)log|sinh(πx/2)|, and gives a general transfer principle for exit distributions of symmetric domains.