Construct a direct correlation-function analogue for general beta

Construct a direct analogue of the Airy-kernel description for the correlation functions of the Airy-beta point process at general beta.

Background

The paper explains that explicit descriptions of the Airy-beta process are scarce beyond the classical beta=2 case, particularly in the multi-time setting. Existing approaches provide stochastic or integral representations, but not a direct correlation-kernel-type formula for general beta.

A direct correlation-function description would provide an explicit counterpart to the determinantal Airy-kernel formalism available at beta=2 and would clarify the structure of Airy-beta statistics for nonclassical beta.

References

To our knowledge, no comparable direct analogue of the Airy kernel is available for the correlation functions at general $\beta$.

— Airy limit for the Jack process and topological expansion  (2609.03532 - Xu, 3 Sep 2026) in Section 1, subsection “Overview”