Soft edge limit of the Laguerre beta-ensemble at the lower edge

Yun Li, Benedek Valkó, Jiaming Xu

We show that the lower edge of the appropriately scaled size $n$ Laguerre beta-ensemble with parameter $a=a_n$ converges to the ${\mathrm{Airy}}_{\beta }$ process as $n\to \infty$ whe…