Fourth-Order Fusion Asymptotics for $\mathrm{Sine}_β$ Correlation Functions

We compute the fourth-order correction to the full-collision asymptotics of the correlation functions of the $\mathrm{Sine}_β$ process. For $m \ge 2$ and $mβ> 3$, the normalized correlation has an expansion through order $ε^4$, with an explicit rational coefficient depending on the centered profile