  In this work we discuss a non-Hermitian system described via a
one-dimensional single-particle tight-binding model, where the non-Hermiticity
is governed by a random nearest-neighbor tunnellings, such that the
left-to-right and right-to-left hopping strengths are unequal. A physical
situation of completely real eigenspectrum arises owing to the Hamiltonian's
tridiagonal matrix structure under a simple \emph {sign conservation} of the
product of the conjugate nearest-neighbor tunnelling terms. The off-diagonal
disorder leads the non-Hermitian system to a localization-delocalization
transition. The emergent nature of the transition is recognized through a
finite-size spectral analysis. A comprehensive scaling theorem is then
developed for characterizing the criticality. We perform careful analysis of
localization length, inverse participation ratio, and energy splitting for
reporting the scaling exponents, which turns out to be different from the ones
in the conventional Anderson localization.

Disordered Systems and Neural Networks;Quantum Physics