  We provide a complete thermodynamic solution of a 1D hopping model in the
presence of a random potential by obtaining the density of states. Since the
partition function is related to the density of states by a Laplace transform,
the density of states determines completely the thermodynamic behavior of the
system. We have also shown that the transfer matrix technique, or the so-called
dynamic programming, used to obtain the density of states in the 1D hopping
model may be generalized to tackle a long-standing problem in statistical
significance assessment for one of the most important proteomic tasks - peptide
sequencing using tandem mass spectrometry data.
