  We study the hard edge limit of a multilevel extension of the Laguerre
$\beta$-ensemble at zero temperature. In particular, we show that
asymptotically the ensemble is given by Gaussians with covariance matrix
expressible in terms of the Fourier-Bessel series. These Gaussians also have an
explicit representation as the partition functions of additive polymers arising
from a random walk on roots of the Bessel functions. Our approach builds off of
the one introduced in arxiv:2009.02006 and is rooted in using the theory of
dual and associated polynomials to diagonalize transition matrices relating
levels of the ensemble.
