# Advanced School on Random Matrices and Growth Models

## Why random matrices share universal processes with interacting particle systems?

**Content:** In these lecture we explain why limiting distribution function, like

the Tracy-Widom distribution, or limit processes, like the Airy_{2} pro-

cess, arise both in random matrices and interacting particle systems.

The link is through a common mathematical structure on an interlac-

ing structure, also known as Gelfand-Tsetlin pattern, that appears for

specific models in both fields.

• | Lecture notes (updated 5. September 2013) |