  We consider two directed polymer models in the Kardar-Parisi-Zhang (KPZ)
universality class: the O'Connell-Yor semi-discrete directed polymer with
boundary sources and the continuum directed random polymer with (m,n)-spiked
boundary perturbations. The free energy of the continuum polymer is the
Hopf-Cole solution of the KPZ equation with the corresponding (m,n)-spiked
initial condition. This new initial condition is constructed using two
semi-discrete polymer models with independent bulk randomness and coupled
boundary sources. We prove that the limiting fluctuations of the free energies
rescaled by the 1/3rd power of time in both polymer models converge to the
Borodin-Peche type deformations of the GUE Tracy-Widom distribution.
