I will discuss a system of N non-intersecting Brownian bridges on the time interval [-1; 1] where N - m paths start and end at the origin and the m top paths go between arbitrary positions. This system is known to generate several universal determinantal processes as scaling limits. I will focus on the distribution of the limiting maximal height for this system, which provides a deformation of the Tracy-Widom GOE distribution in random matrix theory. I will present a Fredholm determinant formula for this distribution function.
I also discuss the connection with KPZ fluctuations, as well as some results on relations with Painleve II and other PDEs. This is based on joint work with Daniel Remenik and Karl Liechty.