# Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution

@article{Liechty2020AiryPW, title={Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution}, author={Karl Liechty and Gia Bao Nguyen and Daniel Remenik}, journal={arXiv: Probability}, year={2020} }

We study the distribution of the supremum of the Airy process with $m$ wanderers minus a parabola, or equivalently the limit of the rescaled maximal height of a system of $N$ non-intersecting Brownian bridges as $N\to\infty$, where the first $N-m$ paths start and end at the origin and the remaining $m$ go between arbitrary positions. The distribution provides a $2m$-parameter deformation of the Tracy--Widom GOE distribution, which is recovered in the limit corresponding to all Brownian paths…

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