  We consider the Plancherel-Rotach type asymptotics of the biorthogonal
polynomials associated to the biorthogonal ensemble with the joint probability
density function
  \begin{equation*}
  \frac{1}{C} \prod_{1 \leq i < j \leq n} (\lambda_j -\lambda_i)(f(\lambda_j) -
f(\lambda_i)) \prod^n_{j = 1} W^{(n)}_{\alpha}(\lambda_j) d\lambda_j,
  \end{equation*}
  where
  \begin{align*}
  f(x) = {}& \sinh^2(\sqrt{x}), & W^{(n)}_{\alpha}(x) = {}& x^{\alpha} h(x)
e^{-nV(x)}.
  \end{align*}
  In the special case that the potential function $V$ is linear, this
biorthogonal ensemble arises in the quantum transport theory of disordered
wires. We analyze the asymptotic problem via $2$-component vector-valued
Riemann-Hilbert problems, and solve it under the one-cut regular with a hard
edge condition.
  As a consequence of our result, we observe that the equilibrium measure of
the biorthogonal ensemble with linear $V$ is the limiting density of particles
in the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation with the ballistic initial
condition.
