Half a decade ago, Praehofer and Spohn discovered the Airy$_2$ process corner growth model. It appeared to be one of the universal processes, appearing in different models including random matrix theory. More recently, we discovered the analogue for growth on a flat substrate: the Airy$_1$ process. This process does not describe only the large time surface statistics at a fixed time, but its universality extends to any “space-like paths”! We will present the result using the totally asymmetric simple exclusion process (TASEP) as reference model, for which the extreme special cases of space-like paths are (a) fixed time, and (b) tagged particle.

Weierstrass Institute, Berlin