  We study the free energy and its relevant quantity for the directed polymer
in random environment. The polymer is allowed to make unbounded jumps and the
environment is given by the Bernoulli variables. We first establish the
concentration of the ground state energy of polymer at zero temperature.
Secondly, we also prove the same property of the free energy at finite
temperature. In the proof, we use the fact that the maximum jump of any polymer
nearly minimizing energy is not too large with high probability. This is an
interesting property itself from the first passage percolation viewpoint.
