Admissible initial data and limiting parameters at soft and hard edges

Determine which prescribed initial configurations and additional limiting data can be incorporated into extended-state and entire-function constructions for \(\beta=2\) Airy dynamics at the soft edge and Bessel dynamics at the hard edge.

Background

The paper’s extended-state and entire-function framework records information lost at infinity for unscaled bulk Dyson Brownian motion at $\beta=2$. The authors suggest analogous constructions for Airy and Bessel dynamics but leave unresolved the precise classes of deterministic initial configurations and additional limiting parameters that can be accommodated at the soft and hard edges.