Large-temperature Poisson limit for the limiting point process

Let $\mathcal{M}_a$ be the limiting point process on $(0,\infty)$, and let $a$ denote the parameter indexing this family. A rescaling of $\mathcal{M}_a$ is understood as in the paper.

Poisson-limit conjecture. When $a\to\infty$, the rescaled point process $\mathcal{M}_a$ converges towards a Poisson point process.

This conjecture predicts Poissonian statistics in the large-$a$ limit, reflecting the strong drift of the coupled diffusions and the transition from the stochastic Bessel operator to the stochastic Airy operator. The precise mode of convergence and the rescaling are not specified in the supplied statement.