Supremum of the Airy2 process minus a parabola on a half line

Details Supremum of the Airy2 process minus a parabola on a half line Supremum of the Airy2 process minus a parabola on a half line

2011-11-10

arxiv.org/abs/1111.2565v1

Mathematics

Probability

Scientific paper

Let $\aip(t)$ be the Airy$_2$ process. We show that the random variable
\[\sup_{t\leq\alpha}\big(\aip(t)-t^2\big)+\min\{0,\alpha\}^2\] has the same
distribution as the one-point marginal of the Airy$_{2\to1}$ process at time
$\alpha$.

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